7x^2-20=31x

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

7x^2-20=31x

We move all terms to the left:

7x^2-20-(31x)=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{-8}{14}
=-4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+39}{2*7}=\frac{70}{14}
=5
$