6=0.01x^2-0.03x+0.45

Solution for 6=0.01x^2-0.03x+0.45 equation:

6=0.01x^2-0.03x+0.45

We move all terms to the left:

6-(0.01x^2-0.03x+0.45)=0

We get rid of parentheses

-0.01x^2+0.03x-0.45+6=0

We add all the numbers together, and all the variables

-0.01x^2+0.03x+5.55=0

a = -0.01; b = 0.03; c = +5.55;
Δ = b2-4ac
Δ = 0.032-4·(-0.01)·5.55
Δ = 0.2229
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{-(0.03)-\sqrt{0.2229}}{2*-0.01}=\frac{-0.03-\sqrt{0.2229}}{-0.02}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.03)+\sqrt{0.2229}}{2*-0.01}=\frac{-0.03+\sqrt{0.2229}}{-0.02}
$