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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(4x(2x+12)), so:

4x(2x+12)

We multiply parentheses

8x^2+48x

Back to the equation:

-(8x^2+48x)


We get rid of parentheses

-8x^2+2x-48x-12=0

We add all the numbers together, and all the variables

-8x^2-46x-12=0

a = -8; b = -46; c = -12;
Δ = b2-4ac
Δ = -462-4·(-8)·(-12)
Δ = 1732
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:

$\sqrt{\Delta}=\sqrt{1732}=\sqrt{4*433}=\sqrt{4}*\sqrt{433}=2\sqrt{433}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{433}}{2*-8}=\frac{46-2\sqrt{433}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{433}}{2*-8}=\frac{46+2\sqrt{433}}{-16}
$