5000=50w+(w*w)

Solution for 5000=50w+(w*w) equation:

5000=50w+(w*w)

We move all terms to the left:

5000-(50w+(w*w))=0

We add all the numbers together, and all the variables

-(50w+(+w*w))+5000=0


We calculate terms in parentheses: -(50w+(+w*w)), so:

50w+(+w*w)

We get rid of parentheses

50w+w*w

Wy multiply elements

w^2+50w

Back to the equation:

-(w^2+50w)


We get rid of parentheses

-w^2-50w+5000=0

We add all the numbers together, and all the variables

-1w^2-50w+5000=0

a = -1; b = -50; c = +5000;
Δ = b2-4ac
Δ = -502-4·(-1)·5000
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-150}{2*-1}=\frac{-100}{-2}
=+50
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+150}{2*-1}=\frac{200}{-2}
=-100
$