3x^-6x^2-27x+54=0

Solution for 3x^-6x^2-27x+54=0 equation:

3x^-6x^2-27x+54=0

We add all the numbers together, and all the variables

-6x^2-24x+54=0

a = -6; b = -24; c = +54;
Δ = b2-4ac
Δ = -242-4·(-6)·54
Δ = 1872
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:

$\sqrt{\Delta}=\sqrt{1872}=\sqrt{144*13}=\sqrt{144}*\sqrt{13}=12\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{13}}{2*-6}=\frac{24-12\sqrt{13}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{13}}{2*-6}=\frac{24+12\sqrt{13}}{-12}
$