16^3-20x^2+6x=0

Solution for 16^3-20x^2+6x=0 equation:

16^3-20x^2+6x=0

We add all the numbers together, and all the variables

-20x^2+6x+4096=0

a = -20; b = 6; c = +4096;
Δ = b2-4ac
Δ = 62-4·(-20)·4096
Δ = 327716
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:

$\sqrt{\Delta}=\sqrt{327716}=\sqrt{4*81929}=\sqrt{4}*\sqrt{81929}=2\sqrt{81929}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{81929}}{2*-20}=\frac{-6-2\sqrt{81929}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{81929}}{2*-20}=\frac{-6+2\sqrt{81929}}{-40}
$