X(x-26)=90

Solution for X(x-26)=90 equation:

X(X-26)=90

We move all terms to the left:

X(X-26)-(90)=0

We multiply parentheses

X^2-26X-90=0

a = 1; b = -26; c = -90;
Δ = b2-4ac
Δ = -262-4·1·(-90)
Δ = 1036
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:

$\sqrt{\Delta}=\sqrt{1036}=\sqrt{4*259}=\sqrt{4}*\sqrt{259}=2\sqrt{259}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{259}}{2*1}=\frac{26-2\sqrt{259}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{259}}{2*1}=\frac{26+2\sqrt{259}}{2}
$