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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -((x+2)2x), so:

(x+2)2x

We multiply parentheses

2x^2+4x

Back to the equation:

-(2x^2+4x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2-12x+12=0

a = -2; b = -12; c = +12;
Δ = b2-4ac
Δ = -122-4·(-2)·12
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{15}}{2*-2}=\frac{12-4\sqrt{15}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{15}}{2*-2}=\frac{12+4\sqrt{15}}{-4}
$