x2+(x+7)2=169

Solution for x2+(x+7)2=169 equation:

x2+(x+7)2=169

We move all terms to the left:

x2+(x+7)2-(169)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

x^2+2x+14-169=0

We add all the numbers together, and all the variables

x^2+2x-155=0

a = 1; b = 2; c = -155;
Δ = b2-4ac
Δ = 22-4·1·(-155)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{39}}{2*1}=\frac{-2-4\sqrt{39}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{39}}{2*1}=\frac{-2+4\sqrt{39}}{2}
$