x(x+300)=400000

Solution for x(x+300)=400000 equation:

x(x+300)=400000

We move all terms to the left:

x(x+300)-(400000)=0

We multiply parentheses

x^2+300x-400000=0

a = 1; b = 300; c = -400000;
Δ = b2-4ac
Δ = 3002-4·1·(-400000)
Δ = 1690000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1690000}=1300$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-1300}{2*1}=\frac{-1600}{2}
=-800
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+1300}{2*1}=\frac{1000}{2}
=500
$