v^2-242=0

Solution for v^2-242=0 equation:

v^2-242=0

a = 1; b = 0; c = -242;
Δ = b2-4ac
Δ = 02-4·1·(-242)
Δ = 968
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{968}=\sqrt{484*2}=\sqrt{484}*\sqrt{2}=22\sqrt{2}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22\sqrt{2}}{2*1}=\frac{0-22\sqrt{2}}{2}
=-\frac{22\sqrt{2}}{2}
=-11\sqrt{2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22\sqrt{2}}{2*1}=\frac{0+22\sqrt{2}}{2}
=\frac{22\sqrt{2}}{2}
=11\sqrt{2}
$