4w^2+52w=120

Solution for 4w^2+52w=120 equation:

4w^2+52w=120

We move all terms to the left:

4w^2+52w-(120)=0

a = 4; b = 52; c = -120;
Δ = b2-4ac
Δ = 522-4·4·(-120)
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-68}{2*4}=\frac{-120}{8}
=-15
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+68}{2*4}=\frac{16}{8}
=2
$