12x^2-48x=3x(x+6)

Solution for 12x^2-48x=3x(x+6) equation:

12x^2-48x=3x(x+6)

We move all terms to the left:

12x^2-48x-(3x(x+6))=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

12x^2-3x^2-48x-18x=0

We add all the numbers together, and all the variables

9x^2-66x=0

a = 9; b = -66; c = 0;
Δ = b2-4ac
Δ = -662-4·9·0
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-66}{2*9}=\frac{0}{18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+66}{2*9}=\frac{132}{18}
=7+1/3
$