5000x-1000x^2=2904

Solution for 5000x-1000x^2=2904 equation:

5000x-1000x^2=2904

We move all terms to the left:

5000x-1000x^2-(2904)=0

a = -1000; b = 5000; c = -2904;
Δ = b2-4ac
Δ = 50002-4·(-1000)·(-2904)
Δ = 13384000
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:

$\sqrt{\Delta}=\sqrt{13384000}=\sqrt{1600*8365}=\sqrt{1600}*\sqrt{8365}=40\sqrt{8365}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5000)-40\sqrt{8365}}{2*-1000}=\frac{-5000-40\sqrt{8365}}{-2000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5000)+40\sqrt{8365}}{2*-1000}=\frac{-5000+40\sqrt{8365}}{-2000}
$