6(x+2)=8x(x+4)

Solution for 6(x+2)=8x(x+4) equation:

6(x+2)=8x(x+4)

We move all terms to the left:

6(x+2)-(8x(x+4))=0

We multiply parentheses

6x-(8x(x+4))+12=0


We calculate terms in parentheses: -(8x(x+4)), so:

8x(x+4)

We multiply parentheses

8x^2+32x

Back to the equation:

-(8x^2+32x)


We get rid of parentheses

-8x^2+6x-32x+12=0

We add all the numbers together, and all the variables

-8x^2-26x+12=0

a = -8; b = -26; c = +12;
Δ = b2-4ac
Δ = -262-4·(-8)·12
Δ = 1060
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:

$\sqrt{\Delta}=\sqrt{1060}=\sqrt{4*265}=\sqrt{4}*\sqrt{265}=2\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{265}}{2*-8}=\frac{26-2\sqrt{265}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{265}}{2*-8}=\frac{26+2\sqrt{265}}{-16}
$