x2+(x+17)2=252

Solution for x2+(x+17)2=252 equation:

x2+(x+17)2=252

We move all terms to the left:

x2+(x+17)2-(252)=0

We add all the numbers together, and all the variables

x^2+(x+17)2-252=0

We multiply parentheses

x^2+2x+34-252=0

We add all the numbers together, and all the variables

x^2+2x-218=0

a = 1; b = 2; c = -218;
Δ = b2-4ac
Δ = 22-4·1·(-218)
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{219}}{2*1}=\frac{-2-2\sqrt{219}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{219}}{2*1}=\frac{-2+2\sqrt{219}}{2}
$