6=-0.01x^2-0.2x+8

Solution for 6=-0.01x^2-0.2x+8 equation:

6=-0.01x^2-0.2x+8

We move all terms to the left:

6-(-0.01x^2-0.2x+8)=0

We get rid of parentheses

0.01x^2+0.2x-8+6=0

We add all the numbers together, and all the variables

0.01x^2+0.2x-2=0

a = 0.01; b = 0.2; c = -2;
Δ = b2-4ac
Δ = 0.22-4·0.01·(-2)
Δ = 0.12
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{-(0.2)-\sqrt{0.12}}{2*0.01}=\frac{-0.2-\sqrt{0.12}}{0.02}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.2)+\sqrt{0.12}}{2*0.01}=\frac{-0.2+\sqrt{0.12}}{0.02}
$