0=-0.05x^2+x+1.89

Solution for 0=-0.05x^2+x+1.89 equation:

0=-0.05x^2+x+1.89

We move all terms to the left:

0-(-0.05x^2+x+1.89)=0

We add all the numbers together, and all the variables

-(-0.05x^2+x+1.89)=0

We get rid of parentheses

0.05x^2-x-1.89=0

We add all the numbers together, and all the variables

0.05x^2-1x-1.89=0

a = 0.05; b = -1; c = -1.89;
Δ = b2-4ac
Δ = -12-4·0.05·(-1.89)
Δ = 1.378
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{-(-1)-\sqrt{1.378}}{2*0.05}=\frac{1-\sqrt{1.378}}{0.1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1.378}}{2*0.05}=\frac{1+\sqrt{1.378}}{0.1}
$