50=(6w-5)(w)

Solution for 50=(6w-5)(w) equation:

50=(6w-5)(w)

We move all terms to the left:

50-((6w-5)(w))=0


We calculate terms in parentheses: -((6w-5)w), so:

(6w-5)w

We multiply parentheses

6w^2-5w

Back to the equation:

-(6w^2-5w)


We get rid of parentheses

-6w^2+5w+50=0

a = -6; b = 5; c = +50;
Δ = b2-4ac
Δ = 52-4·(-6)·50
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-35}{2*-6}=\frac{-40}{-12}
=3+1/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+35}{2*-6}=\frac{30}{-12}
=-2+1/2
$