(2x-3)(x+2)-5(2x-3)=0

Solution for (2x-3)(x+2)-5(2x-3)=0 equation:

(2x-3)(x+2)-5(2x-3)=0

We multiply parentheses

(2x-3)(x+2)-10x+15=0

We multiply parentheses ..

(+2x^2+4x-3x-6)-10x+15=0

We get rid of parentheses

2x^2+4x-3x-10x-6+15=0

We add all the numbers together, and all the variables

2x^2-9x+9=0

a = 2; b = -9; c = +9;
Δ = b2-4ac
Δ = -92-4·2·9
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3}{2*2}=\frac{6}{4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3}{2*2}=\frac{12}{4}
=3
$