18^2=3x^2

Solution for 18^2=3x^2 equation:

18^2=3x^2

We move all terms to the left:

18^2-(3x^2)=0

We add all the numbers together, and all the variables

-3x^2+324=0

a = -3; b = 0; c = +324;
Δ = b2-4ac
Δ = 02-4·(-3)·324
Δ = 3888
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:

$\sqrt{\Delta}=\sqrt{3888}=\sqrt{1296*3}=\sqrt{1296}*\sqrt{3}=36\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{3}}{2*-3}=\frac{0-36\sqrt{3}}{-6}
=-\frac{36\sqrt{3}}{-6}
=-\frac{6\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{3}}{2*-3}=\frac{0+36\sqrt{3}}{-6}
=\frac{36\sqrt{3}}{-6}
=\frac{6\sqrt{3}}{-1}
$