6-2x2=6x

Solution for 6-2x2=6x equation:

6-2x^2=6x

We move all terms to the left:

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

a = -2; b = -6; c = +6;
Δ = b2-4ac
Δ = -62-4·(-2)·6
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{21}}{2*-2}=\frac{6-2\sqrt{21}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{21}}{2*-2}=\frac{6+2\sqrt{21}}{-4}
$