2(x-6)=3x(x+6)

Solution for 2(x-6)=3x(x+6) equation:

2(x-6)=3x(x+6)

We move all terms to the left:

2(x-6)-(3x(x+6))=0

We multiply parentheses

2x-(3x(x+6))-12=0


We calculate terms in parentheses: -(3x(x+6)), so:

3x(x+6)

We multiply parentheses

3x^2+18x

Back to the equation:

-(3x^2+18x)


We get rid of parentheses

-3x^2+2x-18x-12=0

We add all the numbers together, and all the variables

-3x^2-16x-12=0

a = -3; b = -16; c = -12;
Δ = b2-4ac
Δ = -162-4·(-3)·(-12)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{7}}{2*-3}=\frac{16-4\sqrt{7}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{7}}{2*-3}=\frac{16+4\sqrt{7}}{-6}
$