11x^2+66=-77x

Solution for 11x^2+66=-77x equation:

11x^2+66=-77x

We move all terms to the left:

11x^2+66-(-77x)=0

We get rid of parentheses

11x^2+77x+66=0

a = 11; b = 77; c = +66;
Δ = b2-4ac
Δ = 772-4·11·66
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(77)-55}{2*11}=\frac{-132}{22}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(77)+55}{2*11}=\frac{-22}{22}
=-1
$