-5x^2+1000x-30000=0

Solution for -5x^2+1000x-30000=0 equation:

-5x^2+1000x-30000=0

a = -5; b = 1000; c = -30000;
Δ = b2-4ac
Δ = 10002-4·(-5)·(-30000)
Δ = 400000
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:

$\sqrt{\Delta}=\sqrt{400000}=\sqrt{40000*10}=\sqrt{40000}*\sqrt{10}=200\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1000)-200\sqrt{10}}{2*-5}=\frac{-1000-200\sqrt{10}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1000)+200\sqrt{10}}{2*-5}=\frac{-1000+200\sqrt{10}}{-10}
$