12x^2=(2x+6)(x+6)

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

12x^2=(2x+6)(x+6)

We move all terms to the left:

12x^2-((2x+6)(x+6))=0

We multiply parentheses ..

12x^2-((+2x^2+12x+6x+36))=0


We calculate terms in parentheses: -((+2x^2+12x+6x+36)), so:

(+2x^2+12x+6x+36)

We get rid of parentheses

2x^2+12x+6x+36

We add all the numbers together, and all the variables

2x^2+18x+36

Back to the equation:

-(2x^2+18x+36)


We get rid of parentheses

12x^2-2x^2-18x-36=0

We add all the numbers together, and all the variables

10x^2-18x-36=0

a = 10; b = -18; c = -36;
Δ = b2-4ac
Δ = -182-4·10·(-36)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-42}{2*10}=\frac{-24}{20}
=-1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+42}{2*10}=\frac{60}{20}
=3
$