5n^2-31n-20=8

Solution for 5n^2-31n-20=8 equation:

5n^2-31n-20=8

We move all terms to the left:

5n^2-31n-20-(8)=0

We add all the numbers together, and all the variables

5n^2-31n-28=0

a = 5; b = -31; c = -28;
Δ = b2-4ac
Δ = -312-4·5·(-28)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-39}{2*5}=\frac{-8}{10}
=-4/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+39}{2*5}=\frac{70}{10}
=7
$