0.2+10k2+0.4+3k=1

Solution for 0.2+10k2+0.4+3k=1 equation:

0.2+10k^2+0.4+3k=1

We move all terms to the left:

0.2+10k^2+0.4+3k-(1)=0

We add all the numbers together, and all the variables

10k^2+3k-0.4=0

a = 10; b = 3; c = -0.4;
Δ = b2-4ac
Δ = 32-4·10·(-0.4)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-5}{2*10}=\frac{-8}{20}
=-2/5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+5}{2*10}=\frac{2}{20}
=1/10
$