4x(x-32)=0

Solution for 4x(x-32)=0 equation:

4x(x-32)=0

We multiply parentheses

4x^2-128x=0

a = 4; b = -128; c = 0;
Δ = b2-4ac
Δ = -1282-4·4·0
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-128}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+128}{2*4}=\frac{256}{8}
=32
$