X(x+18)=12^2

Solution for X(x+18)=12^2 equation:

X(X+18)=12^2

We move all terms to the left:

X(X+18)-(12^2)=0

We add all the numbers together, and all the variables

X(X+18)-144=0

We multiply parentheses

X^2+18X-144=0

a = 1; b = 18; c = -144;
Δ = b2-4ac
Δ = 182-4·1·(-144)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-30}{2*1}=\frac{-48}{2}
=-24
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+30}{2*1}=\frac{12}{2}
=6
$