(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)+10x+6=0

We get rid of parentheses

-2x^2-6x+5x+10x+15+6=0

We add all the numbers together, and all the variables

-2x^2+9x+21=0

a = -2; b = 9; c = +21;
Δ = b2-4ac
Δ = 92-4·(-2)·21
Δ = 249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{249}}{2*-2}=\frac{-9-\sqrt{249}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{249}}{2*-2}=\frac{-9+\sqrt{249}}{-4}
$