-5000x^2-1000x+12.5=0

Solution for -5000x^2-1000x+12.5=0 equation:

-5000x^2-1000x+12.5=0

a = -5000; b = -1000; c = +12.5;
Δ = b2-4ac
Δ = -10002-4·(-5000)·12.5
Δ = 1250000
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:

$\sqrt{\Delta}=\sqrt{1250000}=\sqrt{250000*5}=\sqrt{250000}*\sqrt{5}=500\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-500\sqrt{5}}{2*-5000}=\frac{1000-500\sqrt{5}}{-10000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+500\sqrt{5}}{2*-5000}=\frac{1000+500\sqrt{5}}{-10000}
$