50625=(w+15)(w)

Solution for 50625=(w+15)(w) equation:

50625=(w+15)(w)

We move all terms to the left:

50625-((w+15)(w))=0


We calculate terms in parentheses: -((w+15)w), so:

(w+15)w

We multiply parentheses

w^2+15w

Back to the equation:

-(w^2+15w)


We get rid of parentheses

-w^2-15w+50625=0

We add all the numbers together, and all the variables

-1w^2-15w+50625=0

a = -1; b = -15; c = +50625;
Δ = b2-4ac
Δ = -152-4·(-1)·50625
Δ = 202725
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{202725}=\sqrt{225*901}=\sqrt{225}*\sqrt{901}=15\sqrt{901}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15\sqrt{901}}{2*-1}=\frac{15-15\sqrt{901}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15\sqrt{901}}{2*-1}=\frac{15+15\sqrt{901}}{-2}
$