x(6x+8)=12

Solution for x(6x+8)=12 equation:

x(6x+8)=12

We move all terms to the left:

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

We multiply parentheses

6x^2+8x-12=0

a = 6; b = 8; c = -12;
Δ = b2-4ac
Δ = 82-4·6·(-12)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{22}}{2*6}=\frac{-8-4\sqrt{22}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{22}}{2*6}=\frac{-8+4\sqrt{22}}{12}
$