X(x+5000)=8400

Solution for X(x+5000)=8400 equation:

X(X+5000)=8400

We move all terms to the left:

X(X+5000)-(8400)=0

We multiply parentheses

X^2+5000X-8400=0

a = 1; b = 5000; c = -8400;
Δ = b2-4ac
Δ = 50002-4·1·(-8400)
Δ = 25033600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{25033600}=\sqrt{1600*15646}=\sqrt{1600}*\sqrt{15646}=40\sqrt{15646}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5000)-40\sqrt{15646}}{2*1}=\frac{-5000-40\sqrt{15646}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5000)+40\sqrt{15646}}{2*1}=\frac{-5000+40\sqrt{15646}}{2}
$