2s^2-3=240

Solution for 2s^2-3=240 equation:

2s^2-3=240

We move all terms to the left:

2s^2-3-(240)=0

We add all the numbers together, and all the variables

2s^2-243=0

a = 2; b = 0; c = -243;
Δ = b2-4ac
Δ = 02-4·2·(-243)
Δ = 1944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1944}=\sqrt{324*6}=\sqrt{324}*\sqrt{6}=18\sqrt{6}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{6}}{2*2}=\frac{0-18\sqrt{6}}{4}
=-\frac{18\sqrt{6}}{4}
=-\frac{9\sqrt{6}}{2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{6}}{2*2}=\frac{0+18\sqrt{6}}{4}
=\frac{18\sqrt{6}}{4}
=\frac{9\sqrt{6}}{2}
$