X2+(x+1)2=305

Solution for X2+(x+1)2=305 equation:

X2+(X+1)2=305

We move all terms to the left:

X2+(X+1)2-(305)=0

We add all the numbers together, and all the variables

X^2+(X+1)2-305=0

We multiply parentheses

X^2+2X+2-305=0

We add all the numbers together, and all the variables

X^2+2X-303=0

a = 1; b = 2; c = -303;
Δ = b2-4ac
Δ = 22-4·1·(-303)
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-8\sqrt{19}}{2*1}=\frac{-2-8\sqrt{19}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8\sqrt{19}}{2*1}=\frac{-2+8\sqrt{19}}{2}
$