2x^2-13x=31=0

Solution for 2x^2-13x=31=0 equation:

2x^2-13x=31=0

We move all terms to the left:

2x^2-13x-(31)=0

a = 2; b = -13; c = -31;
Δ = b2-4ac
Δ = -132-4·2·(-31)
Δ = 417
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{417}}{2*2}=\frac{13-\sqrt{417}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{417}}{2*2}=\frac{13+\sqrt{417}}{4}
$