(x)(x+3)=108^2

Solution for (x)(x+3)=108^2 equation:

(x)(x+3)=108^2

We move all terms to the left:

(x)(x+3)-(108^2)=0

We add all the numbers together, and all the variables

x(x+3)-11664=0

We multiply parentheses

x^2+3x-11664=0

a = 1; b = 3; c = -11664;
Δ = b2-4ac
Δ = 32-4·1·(-11664)
Δ = 46665
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:

$\sqrt{\Delta}=\sqrt{46665}=\sqrt{9*5185}=\sqrt{9}*\sqrt{5185}=3\sqrt{5185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{5185}}{2*1}=\frac{-3-3\sqrt{5185}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{5185}}{2*1}=\frac{-3+3\sqrt{5185}}{2}
$