2x(x+6)+6x+8=4x-12

Solution for 2x(x+6)+6x+8=4x-12 equation:

2x(x+6)+6x+8=4x-12

We move all terms to the left:

2x(x+6)+6x+8-(4x-12)=0

We add all the numbers together, and all the variables

6x+2x(x+6)-(4x-12)+8=0

We multiply parentheses

2x^2+6x+12x-(4x-12)+8=0

We get rid of parentheses

2x^2+6x+12x-4x+12+8=0

We add all the numbers together, and all the variables

2x^2+14x+20=0

a = 2; b = 14; c = +20;
Δ = b2-4ac
Δ = 142-4·2·20
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{-(14)-6}{2*2}=\frac{-20}{4}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6}{2*2}=\frac{-8}{4}
=-2
$