X(x-38)=90

Solution for X(x-38)=90 equation:

X(X-38)=90

We move all terms to the left:

X(X-38)-(90)=0

We multiply parentheses

X^2-38X-90=0

a = 1; b = -38; c = -90;
Δ = b2-4ac
Δ = -382-4·1·(-90)
Δ = 1804
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1804}=\sqrt{4*451}=\sqrt{4}*\sqrt{451}=2\sqrt{451}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{451}}{2*1}=\frac{38-2\sqrt{451}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{451}}{2*1}=\frac{38+2\sqrt{451}}{2}
$