-3x2+18=6x

Solution for -3x2+18=6x equation:

-3x^2+18=6x

We move all terms to the left:

-3x^2+18-(6x)=0

a = -3; b = -6; c = +18;
Δ = b2-4ac
Δ = -62-4·(-3)·18
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{7}}{2*-3}=\frac{6-6\sqrt{7}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{7}}{2*-3}=\frac{6+6\sqrt{7}}{-6}
$