8x^2=54

Solution for 8x^2=54 equation:

8x^2=54

We move all terms to the left:

8x^2-(54)=0

a = 8; b = 0; c = -54;
Δ = b2-4ac
Δ = 02-4·8·(-54)
Δ = 1728
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:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{3}}{2*8}=\frac{0-24\sqrt{3}}{16}
=-\frac{24\sqrt{3}}{16}
=-\frac{3\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{3}}{2*8}=\frac{0+24\sqrt{3}}{16}
=\frac{24\sqrt{3}}{16}
=\frac{3\sqrt{3}}{2}
$