(x)(x+1)=113

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

(x)(x+1)=113

We move all terms to the left:

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

We multiply parentheses

x^2+x-113=0

a = 1; b = 1; c = -113;
Δ = b2-4ac
Δ = 12-4·1·(-113)
Δ = 453
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{453}}{2*1}=\frac{-1-\sqrt{453}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{453}}{2*1}=\frac{-1+\sqrt{453}}{2}
$