(0.1x^2)+200000x+200000=0

Solution for (0.1x^2)+200000x+200000=0 equation:

(0.1x^2)+200000x+200000=0

We add all the numbers together, and all the variables

200000x+(0.1x^2)+200000=0

We get rid of parentheses

0.1x^2+200000x+200000=0

a = 0.1; b = 200000; c = +200000;
Δ = b2-4ac
Δ = 2000002-4·0.1·200000
Δ = 39999920000
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:

$\sqrt{\Delta}=\sqrt{39999920000}=\sqrt{645160000*62}=\sqrt{645160000}*\sqrt{62}=25400\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200000)-25400\sqrt{62}}{2*0.1}=\frac{-200000-25400\sqrt{62}}{0.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200000)+25400\sqrt{62}}{2*0.1}=\frac{-200000+25400\sqrt{62}}{0.2}
$