7x^2-31x-2=0

Solution for 7x^2-31x-2=0 equation:

7x^2-31x-2=0

a = 7; b = -31; c = -2;
Δ = b2-4ac
Δ = -312-4·7·(-2)
Δ = 1017
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:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-3\sqrt{113}}{2*7}=\frac{31-3\sqrt{113}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+3\sqrt{113}}{2*7}=\frac{31+3\sqrt{113}}{14}
$