169=2(x)^2

Solution for 169=2(x)^2 equation:

169=2(x)^2

We move all terms to the left:

169-(2(x)^2)=0

determiningTheFunctionDomain
-2x^2+169=0

a = -2; b = 0; c = +169;
Δ = b2-4ac
Δ = 02-4·(-2)·169
Δ = 1352
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:

$\sqrt{\Delta}=\sqrt{1352}=\sqrt{676*2}=\sqrt{676}*\sqrt{2}=26\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-26\sqrt{2}}{2*-2}=\frac{0-26\sqrt{2}}{-4}
=-\frac{26\sqrt{2}}{-4}
=-\frac{13\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+26\sqrt{2}}{2*-2}=\frac{0+26\sqrt{2}}{-4}
=\frac{26\sqrt{2}}{-4}
=\frac{13\sqrt{2}}{-2}
$