6x+8=3x(4x+6)

Solution for 6x+8=3x(4x+6) equation:

6x+8=3x(4x+6)

We move all terms to the left:

6x+8-(3x(4x+6))=0


We calculate terms in parentheses: -(3x(4x+6)), so:

3x(4x+6)

We multiply parentheses

12x^2+18x

Back to the equation:

-(12x^2+18x)


We get rid of parentheses

-12x^2+6x-18x+8=0

We add all the numbers together, and all the variables

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

a = -12; b = -12; c = +8;
Δ = b2-4ac
Δ = -122-4·(-12)·8
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{33}}{2*-12}=\frac{12-4\sqrt{33}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{33}}{2*-12}=\frac{12+4\sqrt{33}}{-24}
$