0=4w^2-31w-120

Solution for 0=4w^2-31w-120 equation:

0=4w^2-31w-120

We move all terms to the left:

0-(4w^2-31w-120)=0

We add all the numbers together, and all the variables

-(4w^2-31w-120)=0

We get rid of parentheses

-4w^2+31w+120=0

a = -4; b = 31; c = +120;
Δ = b2-4ac
Δ = 312-4·(-4)·120
Δ = 2881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-\sqrt{2881}}{2*-4}=\frac{-31-\sqrt{2881}}{-8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{2881}}{2*-4}=\frac{-31+\sqrt{2881}}{-8}
$