(x+2)(x+3)=8+13x

Solution for (x+2)(x+3)=8+13x equation:

(x+2)(x+3)=8+13x

We move all terms to the left:

(x+2)(x+3)-(8+13x)=0

We add all the numbers together, and all the variables

(x+2)(x+3)-(13x+8)=0

We get rid of parentheses

(x+2)(x+3)-13x-8=0

We multiply parentheses ..

(+x^2+3x+2x+6)-13x-8=0

We get rid of parentheses

x^2+3x+2x-13x+6-8=0

We add all the numbers together, and all the variables

x^2-8x-2=0

a = 1; b = -8; c = -2;
Δ = b2-4ac
Δ = -82-4·1·(-2)
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{-(-8)-6\sqrt{2}}{2*1}=\frac{8-6\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6\sqrt{2}}{2*1}=\frac{8+6\sqrt{2}}{2}
$