12(2x+11)=24x(2x+12)

Solution for 12(2x+11)=24x(2x+12) equation:

12(2x+11)=24x(2x+12)

We move all terms to the left:

12(2x+11)-(24x(2x+12))=0

We multiply parentheses

24x-(24x(2x+12))+132=0


We calculate terms in parentheses: -(24x(2x+12)), so:

24x(2x+12)

We multiply parentheses

48x^2+288x

Back to the equation:

-(48x^2+288x)


We get rid of parentheses

-48x^2+24x-288x+132=0

We add all the numbers together, and all the variables

-48x^2-264x+132=0

a = -48; b = -264; c = +132;
Δ = b2-4ac
Δ = -2642-4·(-48)·132
Δ = 95040
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:

$\sqrt{\Delta}=\sqrt{95040}=\sqrt{576*165}=\sqrt{576}*\sqrt{165}=24\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-264)-24\sqrt{165}}{2*-48}=\frac{264-24\sqrt{165}}{-96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-264)+24\sqrt{165}}{2*-48}=\frac{264+24\sqrt{165}}{-96}
$