X2+(x+6)2=28

Solution for X2+(x+6)2=28 equation:

X2+(X+6)2=28

We move all terms to the left:

X2+(X+6)2-(28)=0

We add all the numbers together, and all the variables

X^2+(X+6)2-28=0

We multiply parentheses

X^2+2X+12-28=0

We add all the numbers together, and all the variables

X^2+2X-16=0

a = 1; b = 2; c = -16;
Δ = b2-4ac
Δ = 22-4·1·(-16)
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{17}}{2*1}=\frac{-2-2\sqrt{17}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{17}}{2*1}=\frac{-2+2\sqrt{17}}{2}
$