3x^2+66=-30x

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

3x^2+66=-30x

We move all terms to the left:

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

We get rid of parentheses

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}
$