x*(x+1)=2652

Solution for x*(x+1)=2652 equation:

x(x+1)=2652

We move all terms to the left:

x(x+1)-(2652)=0

We multiply parentheses

x^2+x-2652=0

a = 1; b = 1; c = -2652;
Δ = b2-4ac
Δ = 12-4·1·(-2652)
Δ = 10609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10609}=103$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-103}{2*1}=\frac{-104}{2}
=-52
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+103}{2*1}=\frac{102}{2}
=51
$