(35-w)*w=300

Solution for (35-w)*w=300 equation:

(35-w)*w=300

We move all terms to the left:

(35-w)*w-(300)=0

We add all the numbers together, and all the variables

(-1w+35)*w-300=0

We multiply parentheses

-1w^2+35w-300=0

a = -1; b = 35; c = -300;
Δ = b2-4ac
Δ = 352-4·(-1)·(-300)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-5}{2*-1}=\frac{-40}{-2}
=+20
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+5}{2*-1}=\frac{-30}{-2}
=+15
$