31x^2-2x-360=0

Solution for 31x^2-2x-360=0 equation:

31x^2-2x-360=0

a = 31; b = -2; c = -360;
Δ = b2-4ac
Δ = -22-4·31·(-360)
Δ = 44644
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:

$\sqrt{\Delta}=\sqrt{44644}=\sqrt{4*11161}=\sqrt{4}*\sqrt{11161}=2\sqrt{11161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{11161}}{2*31}=\frac{2-2\sqrt{11161}}{62}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{11161}}{2*31}=\frac{2+2\sqrt{11161}}{62}
$