61=x^2+7

Solution for 61=x^2+7 equation:

61=x^2+7

We move all terms to the left:

61-(x^2+7)=0

We get rid of parentheses

-x^2-7+61=0

We add all the numbers together, and all the variables

-1x^2+54=0

a = -1; b = 0; c = +54;
Δ = b2-4ac
Δ = 02-4·(-1)·54
Δ = 216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*-1}=\frac{0-6\sqrt{6}}{-2}
=-\frac{6\sqrt{6}}{-2}
=-\frac{3\sqrt{6}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*-1}=\frac{0+6\sqrt{6}}{-2}
=\frac{6\sqrt{6}}{-2}
=\frac{3\sqrt{6}}{-1}
$