3x^2-30x=-66

Solution for 3x^2-30x=-66 equation:

3x^2-30x=-66

We move all terms to the left:

3x^2-30x-(-66)=0

We add all the numbers together, and all the variables

3x^2-30x+66=0

a = 3; b = -30; c = +66;
Δ = b2-4ac
Δ = -302-4·3·66
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{3}}{2*3}=\frac{30-6\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{3}}{2*3}=\frac{30+6\sqrt{3}}{6}
$