(x+1)(x+2)-5(x+2)=0

Solution for (x+1)(x+2)-5(x+2)=0 equation:

(x+1)(x+2)-5(x+2)=0

We multiply parentheses

(x+1)(x+2)-5x-10=0

We multiply parentheses ..

(+x^2+2x+x+2)-5x-10=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-2x-8=0

a = 1; b = -2; c = -8;
Δ = b2-4ac
Δ = -22-4·1·(-8)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6}{2*1}=\frac{8}{2}
=4
$