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

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

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

We move all terms to the left:

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

We use the square of the difference formula

4x^2-((2x-3))-9=0


We calculate terms in parentheses: -((2x-3)), so:

(2x-3)

We get rid of parentheses

2x-3

Back to the equation:

-(2x-3)


We get rid of parentheses

4x^2-2x+3-9=0

We add all the numbers together, and all the variables

4x^2-2x-6=0

a = 4; b = -2; c = -6;
Δ = b2-4ac
Δ = -22-4·4·(-6)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*4}=\frac{-8}{8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*4}=\frac{12}{8}
=1+1/2
$