(x)(x+1)=9506

Solution for (x)(x+1)=9506 equation:

(x)(x+1)=9506

We move all terms to the left:

(x)(x+1)-(9506)=0

We multiply parentheses

x^2+x-9506=0

a = 1; b = 1; c = -9506;
Δ = b2-4ac
Δ = 12-4·1·(-9506)
Δ = 38025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{38025}=195$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-195}{2*1}=\frac{-196}{2}
=-98
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+195}{2*1}=\frac{194}{2}
=97
$