825=x^2-8

Solution for 825=x^2-8 equation:

825=x^2-8

We move all terms to the left:

825-(x^2-8)=0

We get rid of parentheses

-x^2+8+825=0

We add all the numbers together, and all the variables

-1x^2+833=0

a = -1; b = 0; c = +833;
Δ = b2-4ac
Δ = 02-4·(-1)·833
Δ = 3332
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:

$\sqrt{\Delta}=\sqrt{3332}=\sqrt{196*17}=\sqrt{196}*\sqrt{17}=14\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{17}}{2*-1}=\frac{0-14\sqrt{17}}{-2}
=-\frac{14\sqrt{17}}{-2}
=-\frac{7\sqrt{17}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{17}}{2*-1}=\frac{0+14\sqrt{17}}{-2}
=\frac{14\sqrt{17}}{-2}
=\frac{7\sqrt{17}}{-1}
$