.17x(50000-x)=6000

Solution for .17x(50000-x)=6000 equation:

.17x(50000-x)=6000

We move all terms to the left:

.17x(50000-x)-(6000)=0

We add all the numbers together, and all the variables

.17x(-1x+50000)-6000=0

We multiply parentheses

-1x^2+50000x-6000=0

a = -1; b = 50000; c = -6000;
Δ = b2-4ac
Δ = 500002-4·(-1)·(-6000)
Δ = 2499976000
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:

$\sqrt{\Delta}=\sqrt{2499976000}=\sqrt{1600*1562485}=\sqrt{1600}*\sqrt{1562485}=40\sqrt{1562485}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50000)-40\sqrt{1562485}}{2*-1}=\frac{-50000-40\sqrt{1562485}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50000)+40\sqrt{1562485}}{2*-1}=\frac{-50000+40\sqrt{1562485}}{-2}
$