200000=140x-0.02x^2

Solution for 200000=140x-0.02x^2 equation:

200000=140x-0.02x^2

We move all terms to the left:

200000-(140x-0.02x^2)=0

We get rid of parentheses

0.02x^2-140x+200000=0

a = 0.02; b = -140; c = +200000;
Δ = b2-4ac
Δ = -1402-4·0.02·200000
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-60}{2*0.02}=\frac{80}{0.04}
=2000
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+60}{2*0.02}=\frac{200}{0.04}
=5000
$