50=(5+w)w

Solution for 50=(5+w)w equation:

50=(5+w)w

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


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

(w+5)w

We multiply parentheses

w^2+5w

Back to the equation:

-(w^2+5w)


We get rid of parentheses

-w^2-5w+50=0

We add all the numbers together, and all the variables

-1w^2-5w+50=0

a = -1; b = -5; c = +50;
Δ = b2-4ac
Δ = -52-4·(-1)·50
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-15}{2*-1}=\frac{-10}{-2}
=+5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+15}{2*-1}=\frac{20}{-2}
=-10
$