121z^2=2

Solution for 121z^2=2 equation:

121z^2=2

We move all terms to the left:

121z^2-(2)=0

a = 121; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·121·(-2)
Δ = 968
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{968}=\sqrt{484*2}=\sqrt{484}*\sqrt{2}=22\sqrt{2}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22\sqrt{2}}{2*121}=\frac{0-22\sqrt{2}}{242}
=-\frac{22\sqrt{2}}{242}
=-\frac{\sqrt{2}}{11}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22\sqrt{2}}{2*121}=\frac{0+22\sqrt{2}}{242}
=\frac{22\sqrt{2}}{242}
=\frac{\sqrt{2}}{11}
$