0=7x^2-31x-20

Solution for 0=7x^2-31x-20 equation:

0=7x^2-31x-20

We move all terms to the left:

0-(7x^2-31x-20)=0

We add all the numbers together, and all the variables

-(7x^2-31x-20)=0

We get rid of parentheses

-7x^2+31x+20=0

a = -7; b = 31; c = +20;
Δ = b2-4ac
Δ = 312-4·(-7)·20
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-39}{2*-7}=\frac{-70}{-14}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+39}{2*-7}=\frac{8}{-14}
=-4/7
$