12x=4x(x-4)

Solution for 12x=4x(x-4) equation:

12x=4x(x-4)

We move all terms to the left:

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


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

4x(x-4)

We multiply parentheses

4x^2-16x

Back to the equation:

-(4x^2-16x)


We get rid of parentheses

-4x^2+12x+16x=0

We add all the numbers together, and all the variables

-4x^2+28x=0

a = -4; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-4)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-4}=\frac{-56}{-8}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-4}=\frac{0}{-8}
=0
$