11z^2=7=106

Solution for 11z^2=7=106 equation:

11z^2=7=106

We move all terms to the left:

11z^2-(7)=0

a = 11; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·11·(-7)
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{77}}{2*11}=\frac{0-2\sqrt{77}}{22}
=-\frac{2\sqrt{77}}{22}
=-\frac{\sqrt{77}}{11}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{77}}{2*11}=\frac{0+2\sqrt{77}}{22}
=\frac{2\sqrt{77}}{22}
=\frac{\sqrt{77}}{11}
$