69=y^2+6

Solution for 69=y^2+6 equation:

69=y^2+6

We move all terms to the left:

69-(y^2+6)=0

We get rid of parentheses

-y^2-6+69=0

We add all the numbers together, and all the variables

-1y^2+63=0

a = -1; b = 0; c = +63;
Δ = b2-4ac
Δ = 02-4·(-1)·63
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{7}}{2*-1}=\frac{0-6\sqrt{7}}{-2}
=-\frac{6\sqrt{7}}{-2}
=-\frac{3\sqrt{7}}{-1}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{7}}{2*-1}=\frac{0+6\sqrt{7}}{-2}
=\frac{6\sqrt{7}}{-2}
=\frac{3\sqrt{7}}{-1}
$