Hexic Equation Calculator
Plug in the coefficients into each box. If the equation has a 'missing term' (for example, no X2 term), then enter it as a zero.

x6 + x5 + x4 + x3 + x2 + x + = 0

x1: + i
x2: + i
x3: + i
x4: + i
x5: + i
x6: + i

Instructions:
This calculator solves equations of the form Ax6 + Bx5 + Cx4 + Dx3 + Ex2 + Fx + G = 0, so if your equation is not in this form already, perform the necessary algebra to do so. Do not leave the field blank

Due to round-off errors, some answers may be slightly off.

This calculator solves for real and complex roots for a sextic equation in the form of Ax6 + Bx5 + Cx4 + Dx3 + Ex2 + Fx + G = 0 where A, B, C, D, E, F, and G are real numbers and A is non-zero. What this calculator does is computes the first root using Newton's Method (the initial guess is complex). If it converges with a complex root, it prints out its conjugate as a second root; if it converges to a real root, it divides out that root to get a quintic and then gets the second root by running Newton's Method on this quintic. After the two roots are found, it divides the two roots out to get a quartic and solves the quartic using the quartic formula implemented in our Quartic/Cubic/Quadratic Equation Calculator.

Error Codes:
1 - A non-numerical value has been detected in one of the fields. Once removed, you should not get this error.
2 - The constant term is zero, which means that x = 0 is a root to the entered equation. The other 5 roots can be found by factoring out x and plugging in the resulting quintic into the Quintic Equation Calculator. This calculator has had problems with equations that do not have a constant term, so the calculator does not allow.
3 - The Leading coefficient is zero, so the entered equation is not hexic; rather, the entered equation is a quintic (degree 5). Use the Quintic Equation Calculator to solve your equation.
4 - Division by zero occurred when the calculator attempted to compute the first solution. Pressing 'Calculate' again will give a new initial guess and should result in a solution. You may have to press the 'Calculate' again button multiple times. If you are still getting this error code after several attempts, shoot me an e-mail (you can find my e-mail address on the front page).
5 - Division by zero occurred when the calculator attempted to compute the second solution. Pressing 'Calculate' again will give a new initial guess and should result in a solution. You may have to press the 'Calculate' button again more than once. If you are still getting this error code after several attempts, shoot me an e-mail (you can find my e-mail address on the front page).
6 - The x5 coefficient is significantly higher than the others. There are a few precision issues with equations with a high x5 coefficent. After dividing the leading coefficient, the x5 coefficient must be less than 400 times the sum of the other coefficients.
7 - Newton's Method diverged while calculating the first solution or the 6,500 iteration limit has been exceeded. Pressing 'Calculate' again will result in a new random first guess and should result in a solution. You may have to press the 'Calculate' again button multiple times. If you are still getting this error code after several attempts, shoot me an e-mail (you can find my e-mail address on the front page).
8 - Newton's Method diverged while calculating the second solution or the 6,500 iteration limit has been exceeded. Pressing 'Calculate' again will result in a new random first guess and should result in a solution. You may have to press the 'Calculate' again button multiple times. If you are still getting this error code after several attempts, shoot me an e-mail (you can find my e-mail address on the front page).