(x+2)(2x+4)=10x+20

Solution for (x+2)(2x+4)=10x+20 equation:

(x+2)(2x+4)=10x+20

We move all terms to the left:

(x+2)(2x+4)-(10x+20)=0

We get rid of parentheses

(x+2)(2x+4)-10x-20=0

We multiply parentheses ..

(+2x^2+4x+4x+8)-10x-20=0

We get rid of parentheses

2x^2+4x+4x-10x+8-20=0

We add all the numbers together, and all the variables

2x^2-2x-12=0

a = 2; b = -2; c = -12;
Δ = b2-4ac
Δ = -22-4·2·(-12)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*2}=\frac{-8}{4}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*2}=\frac{12}{4}
=3
$