1600x-4x^2=50000

Solution for 1600x-4x^2=50000 equation:

1600x-4x^2=50000

We move all terms to the left:

1600x-4x^2-(50000)=0

a = -4; b = 1600; c = -50000;
Δ = b2-4ac
Δ = 16002-4·(-4)·(-50000)
Δ = 1760000
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:

$\sqrt{\Delta}=\sqrt{1760000}=\sqrt{160000*11}=\sqrt{160000}*\sqrt{11}=400\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1600)-400\sqrt{11}}{2*-4}=\frac{-1600-400\sqrt{11}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1600)+400\sqrt{11}}{2*-4}=\frac{-1600+400\sqrt{11}}{-8}
$