(X+24)(x)=90

Solution for (X+24)(x)=90 equation:

(X+24)(X)=90

We move all terms to the left:

(X+24)(X)-(90)=0

We multiply parentheses

X^2+24X-90=0

a = 1; b = 24; c = -90;
Δ = b2-4ac
Δ = 242-4·1·(-90)
Δ = 936
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:

$\sqrt{\Delta}=\sqrt{936}=\sqrt{36*26}=\sqrt{36}*\sqrt{26}=6\sqrt{26}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{26}}{2*1}=\frac{-24-6\sqrt{26}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{26}}{2*1}=\frac{-24+6\sqrt{26}}{2}
$