w(2w-6)-140=0

Solution for w(2w-6)-140=0 equation:

w(2w-6)-140=0

We multiply parentheses

2w^2-6w-140=0

a = 2; b = -6; c = -140;
Δ = b2-4ac
Δ = -62-4·2·(-140)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-34}{2*2}=\frac{-28}{4}
=-7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+34}{2*2}=\frac{40}{4}
=10
$