27x^2=54

Solution for 27x^2=54 equation:

27x^2=54

We move all terms to the left:

27x^2-(54)=0

a = 27; b = 0; c = -54;
Δ = b2-4ac
Δ = 02-4·27·(-54)
Δ = 5832
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:

$\sqrt{\Delta}=\sqrt{5832}=\sqrt{2916*2}=\sqrt{2916}*\sqrt{2}=54\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-54\sqrt{2}}{2*27}=\frac{0-54\sqrt{2}}{54}
=-\frac{54\sqrt{2}}{54}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+54\sqrt{2}}{2*27}=\frac{0+54\sqrt{2}}{54}
=\frac{54\sqrt{2}}{54}
=\sqrt{2}
$