6=-0.016x^2+0.5x+4.5

Solution for 6=-0.016x^2+0.5x+4.5 equation:

6=-0.016x^2+0.5x+4.5

We move all terms to the left:

6-(-0.016x^2+0.5x+4.5)=0

We get rid of parentheses

0.016x^2-0.5x-4.5+6=0

We add all the numbers together, and all the variables

0.016x^2-0.5x+1.5=0

a = 0.016; b = -0.5; c = +1.5;
Δ = b2-4ac
Δ = -0.52-4·0.016·1.5
Δ = 0.154
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{0.154}}{2*0.016}=\frac{0.5-\sqrt{0.154}}{0.032}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{0.154}}{2*0.016}=\frac{0.5+\sqrt{0.154}}{0.032}
$