x(x+2)=2499

Solution for x(x+2)=2499 equation:

x(x+2)=2499

We move all terms to the left:

x(x+2)-(2499)=0

We multiply parentheses

x^2+2x-2499=0

a = 1; b = 2; c = -2499;
Δ = b2-4ac
Δ = 22-4·1·(-2499)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-100}{2*1}=\frac{-102}{2}
=-51
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+100}{2*1}=\frac{98}{2}
=49
$