6x^2+4x-431=0

Solution for 6x^2+4x-431=0 equation:

6x^2+4x-431=0

a = 6; b = 4; c = -431;
Δ = b2-4ac
Δ = 42-4·6·(-431)
Δ = 10360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10360}=\sqrt{4*2590}=\sqrt{4}*\sqrt{2590}=2\sqrt{2590}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{2590}}{2*6}=\frac{-4-2\sqrt{2590}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{2590}}{2*6}=\frac{-4+2\sqrt{2590}}{12}
$