6x^-18x^2-18x+54=0

Solution for 6x^-18x^2-18x+54=0 equation:

6x^-18x^2-18x+54=0

We add all the numbers together, and all the variables

-18x^2-12x+54=0

a = -18; b = -12; c = +54;
Δ = b2-4ac
Δ = -122-4·(-18)·54
Δ = 4032
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:

$\sqrt{\Delta}=\sqrt{4032}=\sqrt{576*7}=\sqrt{576}*\sqrt{7}=24\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-24\sqrt{7}}{2*-18}=\frac{12-24\sqrt{7}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+24\sqrt{7}}{2*-18}=\frac{12+24\sqrt{7}}{-36}
$