23716=x^2+169

Solution for 23716=x^2+169 equation:

23716=x^2+169

We move all terms to the left:

23716-(x^2+169)=0

We get rid of parentheses

-x^2-169+23716=0

We add all the numbers together, and all the variables

-1x^2+23547=0

a = -1; b = 0; c = +23547;
Δ = b2-4ac
Δ = 02-4·(-1)·23547
Δ = 94188
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:

$\sqrt{\Delta}=\sqrt{94188}=\sqrt{4*23547}=\sqrt{4}*\sqrt{23547}=2\sqrt{23547}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{23547}}{2*-1}=\frac{0-2\sqrt{23547}}{-2}
=-\frac{2\sqrt{23547}}{-2}
=-\frac{\sqrt{23547}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{23547}}{2*-1}=\frac{0+2\sqrt{23547}}{-2}
=\frac{2\sqrt{23547}}{-2}
=\frac{\sqrt{23547}}{-1}
$