0=-0.166x^2+x+4.5

Solution for 0=-0.166x^2+x+4.5 equation:

0=-0.166x^2+x+4.5

We move all terms to the left:

0-(-0.166x^2+x+4.5)=0

We add all the numbers together, and all the variables

-(-0.166x^2+x+4.5)=0

We get rid of parentheses

0.166x^2-x-4.5=0

We add all the numbers together, and all the variables

0.166x^2-1x-4.5=0

a = 0.166; b = -1; c = -4.5;
Δ = b2-4ac
Δ = -12-4·0.166·(-4.5)
Δ = 3.988
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{3.988}}{2*0.166}=\frac{1-\sqrt{3.988}}{0.332}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{3.988}}{2*0.166}=\frac{1+\sqrt{3.988}}{0.332}
$