y^2=77

Solution for y^2=77 equation:

y^2=77

We move all terms to the left:

y^2-(77)=0

a = 1; b = 0; c = -77;
Δ = b2-4ac
Δ = 02-4·1·(-77)
Δ = 308
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:

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