x(100+x)=2400

Solution for x(100+x)=2400 equation:

x(100+x)=2400

We move all terms to the left:

x(100+x)-(2400)=0

We add all the numbers together, and all the variables

x(x+100)-2400=0

We multiply parentheses

x^2+100x-2400=0

a = 1; b = 100; c = -2400;
Δ = b2-4ac
Δ = 1002-4·1·(-2400)
Δ = 19600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19600}=140$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-140}{2*1}=\frac{-240}{2}
=-120
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+140}{2*1}=\frac{40}{2}
=20
$