X2+x2-7+x2+x2-7=169

Solution for X2+x2-7+x2+x2-7=169 equation:

X2+X2-7+X2+X2-7=169

We move all terms to the left:

X2+X2-7+X2+X2-7-(169)=0

We add all the numbers together, and all the variables

4X^2-183=0

a = 4; b = 0; c = -183;
Δ = b2-4ac
Δ = 02-4·4·(-183)
Δ = 2928
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:

$\sqrt{\Delta}=\sqrt{2928}=\sqrt{16*183}=\sqrt{16}*\sqrt{183}=4\sqrt{183}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{183}}{2*4}=\frac{0-4\sqrt{183}}{8}
=-\frac{4\sqrt{183}}{8}
=-\frac{\sqrt{183}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{183}}{2*4}=\frac{0+4\sqrt{183}}{8}
=\frac{4\sqrt{183}}{8}
=\frac{\sqrt{183}}{2}
$