X^2+54=4x^2

Solution for X^2+54=4x^2 equation:

X^2+54=4X^2

We move all terms to the left:

X^2+54-(4X^2)=0

We add all the numbers together, and all the variables

-3X^2+54=0

a = -3; b = 0; c = +54;
Δ = b2-4ac
Δ = 02-4·(-3)·54
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{2}}{2*-3}=\frac{0-18\sqrt{2}}{-6}
=-\frac{18\sqrt{2}}{-6}
=-\frac{3\sqrt{2}}{-1}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{2}}{2*-3}=\frac{0+18\sqrt{2}}{-6}
=\frac{18\sqrt{2}}{-6}
=\frac{3\sqrt{2}}{-1}
$