X(x+27)=90

Solution for X(x+27)=90 equation:

X(X+27)=90

We move all terms to the left:

X(X+27)-(90)=0

We multiply parentheses

X^2+27X-90=0

a = 1; b = 27; c = -90;
Δ = b2-4ac
Δ = 272-4·1·(-90)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-33}{2*1}=\frac{-60}{2}
=-30
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+33}{2*1}=\frac{6}{2}
=3
$