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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+x^2-3x+2x-6)-(2x-5)(x+3)-(x(x-5))=0


We calculate terms in parentheses: -(x(x-5)), so:

x(x-5)

We multiply parentheses

x^2-5x

Back to the equation:

-(x^2-5x)


We get rid of parentheses

x^2-x^2-3x+2x-(2x-5)(x+3)+5x-6=0

We multiply parentheses ..

x^2-x^2-(+2x^2+6x-5x-15)-3x+2x+5x-6=0

We add all the numbers together, and all the variables

-(+2x^2+6x-5x-15)+4x-6=0

We get rid of parentheses

-2x^2-6x+5x+4x+15-6=0

We add all the numbers together, and all the variables

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

a = -2; b = 3; c = +9;
Δ = b2-4ac
Δ = 32-4·(-2)·9
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*-2}=\frac{6}{-4}
=-1+1/2
$