X(x+9)=12^2

Solution for X(x+9)=12^2 equation:

X(X+9)=12^2

We move all terms to the left:

X(X+9)-(12^2)=0

We add all the numbers together, and all the variables

X(X+9)-144=0

We multiply parentheses

X^2+9X-144=0

a = 1; b = 9; c = -144;
Δ = b2-4ac
Δ = 92-4·1·(-144)
Δ = 657
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:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{73}}{2*1}=\frac{-9-3\sqrt{73}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{73}}{2*1}=\frac{-9+3\sqrt{73}}{2}
$