4x^2-6=54

Solution for 4x^2-6=54 equation:

4x^2-6=54

We move all terms to the left:

4x^2-6-(54)=0

We add all the numbers together, and all the variables

4x^2-60=0

a = 4; b = 0; c = -60;
Δ = b2-4ac
Δ = 02-4·4·(-60)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{15}}{2*4}=\frac{0-8\sqrt{15}}{8}
=-\frac{8\sqrt{15}}{8}
=-\sqrt{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*4}=\frac{0+8\sqrt{15}}{8}
=\frac{8\sqrt{15}}{8}
=\sqrt{15}
$