4^3-24x^2+48x=0

Solution for 4^3-24x^2+48x=0 equation:

4^3-24x^2+48x=0

We add all the numbers together, and all the variables

-24x^2+48x+64=0

a = -24; b = 48; c = +64;
Δ = b2-4ac
Δ = 482-4·(-24)·64
Δ = 8448
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8448}=\sqrt{256*33}=\sqrt{256}*\sqrt{33}=16\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-16\sqrt{33}}{2*-24}=\frac{-48-16\sqrt{33}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+16\sqrt{33}}{2*-24}=\frac{-48+16\sqrt{33}}{-48}
$