6x=32-6x^2

Solution for 6x=32-6x^2 equation:

6x=32-6x^2

We move all terms to the left:

6x-(32-6x^2)=0

We get rid of parentheses

6x^2+6x-32=0

a = 6; b = 6; c = -32;
Δ = b2-4ac
Δ = 62-4·6·(-32)
Δ = 804
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:

$\sqrt{\Delta}=\sqrt{804}=\sqrt{4*201}=\sqrt{4}*\sqrt{201}=2\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{201}}{2*6}=\frac{-6-2\sqrt{201}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{201}}{2*6}=\frac{-6+2\sqrt{201}}{12}
$