54^3-15x^2-6x=0

Solution for 54^3-15x^2-6x=0 equation:

54^3-15x^2-6x=0

We add all the numbers together, and all the variables

-15x^2-6x+157464=0

a = -15; b = -6; c = +157464;
Δ = b2-4ac
Δ = -62-4·(-15)·157464
Δ = 9447876
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:

$\sqrt{\Delta}=\sqrt{9447876}=\sqrt{36*262441}=\sqrt{36}*\sqrt{262441}=6\sqrt{262441}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{262441}}{2*-15}=\frac{6-6\sqrt{262441}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{262441}}{2*-15}=\frac{6+6\sqrt{262441}}{-30}
$