(3w-4)w=64

Solution for (3w-4)w=64 equation:

(3w-4)w=64

We move all terms to the left:

(3w-4)w-(64)=0

We multiply parentheses

3w^2-4w-64=0

a = 3; b = -4; c = -64;
Δ = b2-4ac
Δ = -42-4·3·(-64)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-28}{2*3}=\frac{-24}{6}
=-4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+28}{2*3}=\frac{32}{6}
=5+1/3
$