(2x+9)(x-9)=108

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

(2x+9)(x-9)=108

We move all terms to the left:

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

We multiply parentheses ..

(+2x^2-18x+9x-81)-108=0

We get rid of parentheses

2x^2-18x+9x-81-108=0

We add all the numbers together, and all the variables

2x^2-9x-189=0

a = 2; b = -9; c = -189;
Δ = b2-4ac
Δ = -92-4·2·(-189)
Δ = 1593
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:

$\sqrt{\Delta}=\sqrt{1593}=\sqrt{9*177}=\sqrt{9}*\sqrt{177}=3\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{177}}{2*2}=\frac{9-3\sqrt{177}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{177}}{2*2}=\frac{9+3\sqrt{177}}{4}
$