(3w-5)w=50

Solution for (3w-5)w=50 equation:

(3w-5)w=50

We move all terms to the left:

(3w-5)w-(50)=0

We multiply parentheses

3w^2-5w-50=0

a = 3; b = -5; c = -50;
Δ = b2-4ac
Δ = -52-4·3·(-50)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-25}{2*3}=\frac{-20}{6}
=-3+1/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+25}{2*3}=\frac{30}{6}
=5
$