-11w^2-7w+120=0

Solution for -11w^2-7w+120=0 equation:

-11w^2-7w+120=0

a = -11; b = -7; c = +120;
Δ = b2-4ac
Δ = -72-4·(-11)·120
Δ = 5329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5329}=73$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-73}{2*-11}=\frac{-66}{-22}
=+3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+73}{2*-11}=\frac{80}{-22}
=-3+7/11
$