5(2x+9)(2x+6)=108

Solution for 5(2x+9)(2x+6)=108 equation:

5(2x+9)(2x+6)=108

We move all terms to the left:

5(2x+9)(2x+6)-(108)=0

We multiply parentheses ..

5(+4x^2+12x+18x+54)-108=0

We multiply parentheses

20x^2+60x+90x+270-108=0

We add all the numbers together, and all the variables

20x^2+150x+162=0

a = 20; b = 150; c = +162;
Δ = b2-4ac
Δ = 1502-4·20·162
Δ = 9540
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:

$\sqrt{\Delta}=\sqrt{9540}=\sqrt{36*265}=\sqrt{36}*\sqrt{265}=6\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-6\sqrt{265}}{2*20}=\frac{-150-6\sqrt{265}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+6\sqrt{265}}{2*20}=\frac{-150+6\sqrt{265}}{40}
$