-x^2+1000x+5000=0

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

-x^2+1000x+5000=0

We add all the numbers together, and all the variables

-1x^2+1000x+5000=0

a = -1; b = 1000; c = +5000;
Δ = b2-4ac
Δ = 10002-4·(-1)·5000
Δ = 1020000
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:

$\sqrt{\Delta}=\sqrt{1020000}=\sqrt{10000*102}=\sqrt{10000}*\sqrt{102}=100\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1000)-100\sqrt{102}}{2*-1}=\frac{-1000-100\sqrt{102}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1000)+100\sqrt{102}}{2*-1}=\frac{-1000+100\sqrt{102}}{-2}
$