(x+2)2+(x)2=394

Solution for (x+2)2+(x)2=394 equation:

(x+2)2+(x)2=394

We move all terms to the left:

(x+2)2+(x)2-(394)=0

We add all the numbers together, and all the variables

x^2+(x+2)2-394=0

We multiply parentheses

x^2+2x+4-394=0

We add all the numbers together, and all the variables

x^2+2x-390=0

a = 1; b = 2; c = -390;
Δ = b2-4ac
Δ = 22-4·1·(-390)
Δ = 1564
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:

$\sqrt{\Delta}=\sqrt{1564}=\sqrt{4*391}=\sqrt{4}*\sqrt{391}=2\sqrt{391}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{391}}{2*1}=\frac{-2-2\sqrt{391}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{391}}{2*1}=\frac{-2+2\sqrt{391}}{2}
$