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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

X^2-3X+2X-6-9=0

We add all the numbers together, and all the variables

X^2-1X-15=0

a = 1; b = -1; c = -15;
Δ = b2-4ac
Δ = -12-4·1·(-15)
Δ = 61
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{-(-1)-\sqrt{61}}{2*1}=\frac{1-\sqrt{61}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{61}}{2*1}=\frac{1+\sqrt{61}}{2}
$