243=8x^2

Solution for 243=8x^2 equation:

243=8x^2

We move all terms to the left:

243-(8x^2)=0

a = -8; b = 0; c = +243;
Δ = b2-4ac
Δ = 02-4·(-8)·243
Δ = 7776
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:

$\sqrt{\Delta}=\sqrt{7776}=\sqrt{1296*6}=\sqrt{1296}*\sqrt{6}=36\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{6}}{2*-8}=\frac{0-36\sqrt{6}}{-16}
=-\frac{36\sqrt{6}}{-16}
=-\frac{9\sqrt{6}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{6}}{2*-8}=\frac{0+36\sqrt{6}}{-16}
=\frac{36\sqrt{6}}{-16}
=\frac{9\sqrt{6}}{-4}
$