x^2+(x+1)=113

Solution for x^2+(x+1)=113 equation:

x^2+(x+1)=113

We move all terms to the left:

x^2+(x+1)-(113)=0

We get rid of parentheses

x^2+x+1-113=0

We add all the numbers together, and all the variables

x^2+x-112=0

a = 1; b = 1; c = -112;
Δ = b2-4ac
Δ = 12-4·1·(-112)
Δ = 449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{449}}{2*1}=\frac{-1-\sqrt{449}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{449}}{2*1}=\frac{-1+\sqrt{449}}{2}
$