0=18x^2-54x+12

Solution for 0=18x^2-54x+12 equation:

0=18x^2-54x+12

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

a = -18; b = 54; c = -12;
Δ = b2-4ac
Δ = 542-4·(-18)·(-12)
Δ = 2052
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:

$\sqrt{\Delta}=\sqrt{2052}=\sqrt{36*57}=\sqrt{36}*\sqrt{57}=6\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6\sqrt{57}}{2*-18}=\frac{-54-6\sqrt{57}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6\sqrt{57}}{2*-18}=\frac{-54+6\sqrt{57}}{-36}
$