-x^2/1000+8x-5000=0

Solution for -x^2/1000+8x-5000=0 equation:

-x^2/1000+8x-5000=0

We multiply all the terms by the denominator


-x^2+8x*1000-5000*1000=0

We add all the numbers together, and all the variables

-1x^2+8x*1000-5000000=0

Wy multiply elements

-1x^2+8000x-5000000=0

a = -1; b = 8000; c = -5000000;
Δ = b2-4ac
Δ = 80002-4·(-1)·(-5000000)
Δ = 44000000
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:

$\sqrt{\Delta}=\sqrt{44000000}=\sqrt{4000000*11}=\sqrt{4000000}*\sqrt{11}=2000\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8000)-2000\sqrt{11}}{2*-1}=\frac{-8000-2000\sqrt{11}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8000)+2000\sqrt{11}}{2*-1}=\frac{-8000+2000\sqrt{11}}{-2}
$