100-0.2x-0.0003x^2=0

Solution for 100-0.2x-0.0003x^2=0 equation:

100-0.2x-0.0003x^2=0

a = -0.0003; b = -0.2; c = +100;
Δ = b2-4ac
Δ = -0.22-4·(-0.0003)·100
Δ = 0.16
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{-(-0.2)-\sqrt{0.16}}{2*-0.0003}=\frac{0.2-\sqrt{0.16}}{-0.0006}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.2)+\sqrt{0.16}}{2*-0.0003}=\frac{0.2+\sqrt{0.16}}{-0.0006}
$