(x+2)(x-3)=x+9

Solution for (x+2)(x-3)=x+9 equation:

(x+2)(x-3)=x+9

We move all terms to the left:

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

We get rid of parentheses

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

We multiply parentheses ..

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

We add all the numbers together, and all the variables

(+x^2-3x+2x-6)-1x-9=0

We get rid of parentheses

x^2-3x+2x-1x-6-9=0

We add all the numbers together, and all the variables

x^2-2x-15=0

a = 1; b = -2; c = -15;
Δ = b2-4ac
Δ = -22-4·1·(-15)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-8}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8}{2*1}=\frac{10}{2}
=5
$