x(x+1)=2162

Solution for x(x+1)=2162 equation:

x(x+1)=2162

We move all terms to the left:

x(x+1)-(2162)=0

We multiply parentheses

x^2+x-2162=0

a = 1; b = 1; c = -2162;
Δ = b2-4ac
Δ = 12-4·1·(-2162)
Δ = 8649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8649}=93$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-93}{2*1}=\frac{-94}{2}
=-47
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+93}{2*1}=\frac{92}{2}
=46
$