n^2=-13n+90

Solution for n^2=-13n+90 equation:

n^2=-13n+90

We move all terms to the left:

n^2-(-13n+90)=0

We get rid of parentheses

n^2+13n-90=0

a = 1; b = 13; c = -90;
Δ = b2-4ac
Δ = 132-4·1·(-90)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-23}{2*1}=\frac{-36}{2}
=-18
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+23}{2*1}=\frac{10}{2}
=5
$