4(3x-12)=12x(x-12)

Solution for 4(3x-12)=12x(x-12) equation:

4(3x-12)=12x(x-12)

We move all terms to the left:

4(3x-12)-(12x(x-12))=0

We multiply parentheses

12x-(12x(x-12))-48=0


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

12x(x-12)

We multiply parentheses

12x^2-144x

Back to the equation:

-(12x^2-144x)


We get rid of parentheses

-12x^2+12x+144x-48=0

We add all the numbers together, and all the variables

-12x^2+156x-48=0

a = -12; b = 156; c = -48;
Δ = b2-4ac
Δ = 1562-4·(-12)·(-48)
Δ = 22032
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:

$\sqrt{\Delta}=\sqrt{22032}=\sqrt{1296*17}=\sqrt{1296}*\sqrt{17}=36\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(156)-36\sqrt{17}}{2*-12}=\frac{-156-36\sqrt{17}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(156)+36\sqrt{17}}{2*-12}=\frac{-156+36\sqrt{17}}{-24}
$