x(2x+3)=108

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

x(2x+3)=108

We move all terms to the left:

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

We multiply parentheses

2x^2+3x-108=0

a = 2; b = 3; c = -108;
Δ = b2-4ac
Δ = 32-4·2·(-108)
Δ = 873
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:

$\sqrt{\Delta}=\sqrt{873}=\sqrt{9*97}=\sqrt{9}*\sqrt{97}=3\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{97}}{2*2}=\frac{-3-3\sqrt{97}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{97}}{2*2}=\frac{-3+3\sqrt{97}}{4}
$