4(x+3)2x=4x-8

Solution for 4(x+3)2x=4x-8 equation:

4(x+3)2x=4x-8

We move all terms to the left:

4(x+3)2x-(4x-8)=0

We multiply parentheses

8x^2+24x-(4x-8)=0

We get rid of parentheses

8x^2+24x-4x+8=0

We add all the numbers together, and all the variables

8x^2+20x+8=0

a = 8; b = 20; c = +8;
Δ = b2-4ac
Δ = 202-4·8·8
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-12}{2*8}=\frac{-32}{16}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+12}{2*8}=\frac{-8}{16}
=-1/2
$