y^2=243

Solution for y^2=243 equation:

y^2=243

We move all terms to the left:

y^2-(243)=0

a = 1; b = 0; c = -243;
Δ = b2-4ac
Δ = 02-4·1·(-243)
Δ = 972
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{3}}{2*1}=\frac{0-18\sqrt{3}}{2}
=-\frac{18\sqrt{3}}{2}
=-9\sqrt{3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{3}}{2*1}=\frac{0+18\sqrt{3}}{2}
=\frac{18\sqrt{3}}{2}
=9\sqrt{3}
$