x(x+13)=90

Solution for x(x+13)=90 equation:

x(x+13)=90

We move all terms to the left:

x(x+13)-(90)=0

We multiply parentheses

x^2+13x-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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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