97=y^2+7

Solution for 97=y^2+7 equation:

97=y^2+7

We move all terms to the left:

97-(y^2+7)=0

We get rid of parentheses

-y^2-7+97=0

We add all the numbers together, and all the variables

-1y^2+90=0

a = -1; b = 0; c = +90;
Δ = b2-4ac
Δ = 02-4·(-1)·90
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{10}}{2*-1}=\frac{0-6\sqrt{10}}{-2}
=-\frac{6\sqrt{10}}{-2}
=-\frac{3\sqrt{10}}{-1}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{10}}{2*-1}=\frac{0+6\sqrt{10}}{-2}
=\frac{6\sqrt{10}}{-2}
=\frac{3\sqrt{10}}{-1}
$