6x2=192+6x

Solution for 6x2=192+6x equation:

6x^2=192+6x

We move all terms to the left:

6x^2-(192+6x)=0

We add all the numbers together, and all the variables

6x^2-(6x+192)=0

We get rid of parentheses

6x^2-6x-192=0

a = 6; b = -6; c = -192;
Δ = b2-4ac
Δ = -62-4·6·(-192)
Δ = 4644
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:

$\sqrt{\Delta}=\sqrt{4644}=\sqrt{36*129}=\sqrt{36}*\sqrt{129}=6\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{129}}{2*6}=\frac{6-6\sqrt{129}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{129}}{2*6}=\frac{6+6\sqrt{129}}{12}
$