6x^2+180=-66x

Solution for 6x^2+180=-66x equation:

6x^2+180=-66x

We move all terms to the left:

6x^2+180-(-66x)=0

We get rid of parentheses

6x^2+66x+180=0

a = 6; b = 66; c = +180;
Δ = b2-4ac
Δ = 662-4·6·180
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-6}{2*6}=\frac{-72}{12}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+6}{2*6}=\frac{-60}{12}
=-5
$