3x^2-3=3x

Solution for 3x^2-3=3x equation:

3x^2-3=3x

We move all terms to the left:

3x^2-3-(3x)=0

a = 3; b = -3; c = -3;
Δ = b2-4ac
Δ = -32-4·3·(-3)
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{5}}{2*3}=\frac{3-3\sqrt{5}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{5}}{2*3}=\frac{3+3\sqrt{5}}{6}
$