3x(6x+2)=6(2x)+8

Solution for 3x(6x+2)=6(2x)+8 equation:

3x(6x+2)=6(2x)+8

We move all terms to the left:

3x(6x+2)-(6(2x)+8)=0

We multiply parentheses

18x^2+6x-(62x+8)=0

We get rid of parentheses

18x^2+6x-62x-8=0

We add all the numbers together, and all the variables

18x^2-56x-8=0

a = 18; b = -56; c = -8;
Δ = b2-4ac
Δ = -562-4·18·(-8)
Δ = 3712
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:

$\sqrt{\Delta}=\sqrt{3712}=\sqrt{64*58}=\sqrt{64}*\sqrt{58}=8\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{58}}{2*18}=\frac{56-8\sqrt{58}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{58}}{2*18}=\frac{56+8\sqrt{58}}{36}
$