X2+(x+1)2=85

Solution for X2+(x+1)2=85 equation:

X2+(X+1)2=85

We move all terms to the left:

X2+(X+1)2-(85)=0

We add all the numbers together, and all the variables

X^2+(X+1)2-85=0

We multiply parentheses

X^2+2X+2-85=0

We add all the numbers together, and all the variables

X^2+2X-83=0

a = 1; b = 2; c = -83;
Δ = b2-4ac
Δ = 22-4·1·(-83)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{21}}{2*1}=\frac{-2-4\sqrt{21}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{21}}{2*1}=\frac{-2+4\sqrt{21}}{2}
$