2n^2=36n+80

Solution for 2n^2=36n+80 equation:

2n^2=36n+80

We move all terms to the left:

2n^2-(36n+80)=0

We get rid of parentheses

2n^2-36n-80=0

a = 2; b = -36; c = -80;
Δ = b2-4ac
Δ = -362-4·2·(-80)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-44}{2*2}=\frac{-8}{4}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+44}{2*2}=\frac{80}{4}
=20
$