w(2w-10)=1500

Solution for w(2w-10)=1500 equation:

w(2w-10)=1500

We move all terms to the left:

w(2w-10)-(1500)=0

We multiply parentheses

2w^2-10w-1500=0

a = 2; b = -10; c = -1500;
Δ = b2-4ac
Δ = -102-4·2·(-1500)
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-110}{2*2}=\frac{-100}{4}
=-25
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+110}{2*2}=\frac{120}{4}
=30
$