x^2+x^2-2x+7=169

Solution for x^2+x^2-2x+7=169 equation:

x^2+x^2-2x+7=169

We move all terms to the left:

x^2+x^2-2x+7-(169)=0

We add all the numbers together, and all the variables

2x^2-2x-162=0

a = 2; b = -2; c = -162;
Δ = b2-4ac
Δ = -22-4·2·(-162)
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10\sqrt{13}}{2*2}=\frac{2-10\sqrt{13}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10\sqrt{13}}{2*2}=\frac{2+10\sqrt{13}}{4}
$