x*(x+1)=2400

Solution for x*(x+1)=2400 equation:

x*(x+1)=2400

We move all terms to the left:

x*(x+1)-(2400)=0

We multiply parentheses

x^2+x-2400=0

a = 1; b = 1; c = -2400;
Δ = b2-4ac
Δ = 12-4·1·(-2400)
Δ = 9601
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{9601}}{2*1}=\frac{-1-\sqrt{9601}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{9601}}{2*1}=\frac{-1+\sqrt{9601}}{2}
$