7w(3w-8)=0

Solution for 7w(3w-8)=0 equation:

7w(3w-8)=0

We multiply parentheses

21w^2-56w=0

a = 21; b = -56; c = 0;
Δ = b2-4ac
Δ = -562-4·21·0
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-56}{2*21}=\frac{0}{42}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+56}{2*21}=\frac{112}{42}
=2+2/3
$