6x(x+6)=(2x+4)(x+6)

Solution for 6x(x+6)=(2x+4)(x+6) equation:

6x(x+6)=(2x+4)(x+6)

We move all terms to the left:

6x(x+6)-((2x+4)(x+6))=0

We multiply parentheses

6x^2+36x-((2x+4)(x+6))=0

We multiply parentheses ..

6x^2-((+2x^2+12x+4x+24))+36x=0


We calculate terms in parentheses: -((+2x^2+12x+4x+24)), so:

(+2x^2+12x+4x+24)

We get rid of parentheses

2x^2+12x+4x+24

We add all the numbers together, and all the variables

2x^2+16x+24

Back to the equation:

-(2x^2+16x+24)


We add all the numbers together, and all the variables

6x^2+36x-(2x^2+16x+24)=0

We get rid of parentheses

6x^2-2x^2+36x-16x-24=0

We add all the numbers together, and all the variables

4x^2+20x-24=0

a = 4; b = 20; c = -24;
Δ = b2-4ac
Δ = 202-4·4·(-24)
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{-(20)-28}{2*4}=\frac{-48}{8}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+28}{2*4}=\frac{8}{8}
=1
$