0=-0.01x^2+0.5x+5.9

Solution for 0=-0.01x^2+0.5x+5.9 equation:

0=-0.01x^2+0.5x+5.9

We move all terms to the left:

0-(-0.01x^2+0.5x+5.9)=0

We add all the numbers together, and all the variables

-(-0.01x^2+0.5x+5.9)=0

We get rid of parentheses

0.01x^2-0.5x-5.9=0

a = 0.01; b = -0.5; c = -5.9;
Δ = b2-4ac
Δ = -0.52-4·0.01·(-5.9)
Δ = 0.486
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{-(-0.5)-\sqrt{0.486}}{2*0.01}=\frac{0.5-\sqrt{0.486}}{0.02}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{0.486}}{2*0.01}=\frac{0.5+\sqrt{0.486}}{0.02}
$