(2x-3)(2x-3)=135

Solution for (2x-3)(2x-3)=135 equation:

(2x-3)(2x-3)=135

We move all terms to the left:

(2x-3)(2x-3)-(135)=0

We multiply parentheses ..

(+4x^2-6x-6x+9)-135=0

We get rid of parentheses

4x^2-6x-6x+9-135=0

We add all the numbers together, and all the variables

4x^2-12x-126=0

a = 4; b = -12; c = -126;
Δ = b2-4ac
Δ = -122-4·4·(-126)
Δ = 2160
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:

$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{15}}{2*4}=\frac{12-12\sqrt{15}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{15}}{2*4}=\frac{12+12\sqrt{15}}{8}
$