12x(2x-2)=3x(x+4)

Solution for 12x(2x-2)=3x(x+4) equation:

12x(2x-2)=3x(x+4)

We move all terms to the left:

12x(2x-2)-(3x(x+4))=0

We multiply parentheses

24x^2-24x-(3x(x+4))=0


We calculate terms in parentheses: -(3x(x+4)), so:

3x(x+4)

We multiply parentheses

3x^2+12x

Back to the equation:

-(3x^2+12x)


We get rid of parentheses

24x^2-3x^2-24x-12x=0

We add all the numbers together, and all the variables

21x^2-36x=0

a = 21; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·21·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*21}=\frac{0}{42}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*21}=\frac{72}{42}
=1+5/7
$