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

Solution for (2x+3)(2x-3)+(x-2)(2x+3)=0 equation:

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

We use the square of the difference formula

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

We multiply parentheses ..

4x^2+(+2x^2+3x-4x-6)-9=0

We get rid of parentheses

4x^2+2x^2+3x-4x-6-9=0

We add all the numbers together, and all the variables

6x^2-1x-15=0

a = 6; b = -1; c = -15;
Δ = b2-4ac
Δ = -12-4·6·(-15)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-19}{2*6}=\frac{-18}{12}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+19}{2*6}=\frac{20}{12}
=1+2/3
$