x2+(x+1)2=145

Solution for x2+(x+1)2=145 equation:

x2+(x+1)2=145

We move all terms to the left:

x2+(x+1)2-(145)=0

We add all the numbers together, and all the variables

x^2+(x+1)2-145=0

We multiply parentheses

x^2+2x+2-145=0

We add all the numbers together, and all the variables

x^2+2x-143=0

a = 1; b = 2; c = -143;
Δ = b2-4ac
Δ = 22-4·1·(-143)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-24}{2*1}=\frac{-26}{2}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+24}{2*1}=\frac{22}{2}
=11
$