500x^2-x-5=0

Solution for 500x^2-x-5=0 equation:

500x^2-x-5=0

We add all the numbers together, and all the variables

500x^2-1x-5=0

a = 500; b = -1; c = -5;
Δ = b2-4ac
Δ = -12-4·500·(-5)
Δ = 10001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{10001}}{2*500}=\frac{1-\sqrt{10001}}{1000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{10001}}{2*500}=\frac{1+\sqrt{10001}}{1000}
$