6=0,12a^2-0,08a+0,16

Solution for 6=0,12a^2-0,08a+0,16 equation:

6=0.12a^2-0.08a+0.16

We move all terms to the left:

6-(0.12a^2-0.08a+0.16)=0

We get rid of parentheses

-0.12a^2+0.08a-0.16+6=0

We add all the numbers together, and all the variables

-0.12a^2+0.08a+5.84=0

a = -0.12; b = 0.08; c = +5.84;
Δ = b2-4ac
Δ = 0.082-4·(-0.12)·5.84
Δ = 2.8096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.08)-\sqrt{2.8096}}{2*-0.12}=\frac{-0.08-\sqrt{2.8096}}{-0.24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.08)+\sqrt{2.8096}}{2*-0.12}=\frac{-0.08+\sqrt{2.8096}}{-0.24}
$