(X+2)(x-3)=11+x

Solution for (X+2)(x-3)=11+x equation:

(X+2)(X-3)=11+X

We move all terms to the left:

(X+2)(X-3)-(11+X)=0

We add all the numbers together, and all the variables

(X+2)(X-3)-(X+11)=0

We get rid of parentheses

(X+2)(X-3)-X-11=0

We multiply parentheses ..

(+X^2-3X+2X-6)-X-11=0

We add all the numbers together, and all the variables

(+X^2-3X+2X-6)-1X-11=0

We get rid of parentheses

X^2-3X+2X-1X-6-11=0

We add all the numbers together, and all the variables

X^2-2X-17=0

a = 1; b = -2; c = -17;
Δ = b2-4ac
Δ = -22-4·1·(-17)
Δ = 72
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{2}}{2*1}=\frac{2-6\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{2}}{2*1}=\frac{2+6\sqrt{2}}{2}
$