x(x+1)=9312

Solution for x(x+1)=9312 equation:

x(x+1)=9312

We move all terms to the left:

x(x+1)-(9312)=0

We multiply parentheses

x^2+x-9312=0

a = 1; b = 1; c = -9312;
Δ = b2-4ac
Δ = 12-4·1·(-9312)
Δ = 37249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{37249}=193$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-193}{2*1}=\frac{-194}{2}
=-97
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+193}{2*1}=\frac{192}{2}
=96
$