5x^2+200000x-100000=0

Solution for 5x^2+200000x-100000=0 equation:

5x^2+200000x-100000=0

a = 5; b = 200000; c = -100000;
Δ = b2-4ac
Δ = 2000002-4·5·(-100000)
Δ = 40002000000
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:

$\sqrt{\Delta}=\sqrt{40002000000}=\sqrt{1000000*40002}=\sqrt{1000000}*\sqrt{40002}=1000\sqrt{40002}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200000)-1000\sqrt{40002}}{2*5}=\frac{-200000-1000\sqrt{40002}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200000)+1000\sqrt{40002}}{2*5}=\frac{-200000+1000\sqrt{40002}}{10}
$