5k^2+k=0.4

Solution for 5k^2+k=0.4 equation:

5k^2+k=0.4

We move all terms to the left:

5k^2+k-(0.4)=0

We add all the numbers together, and all the variables

5k^2+k-0.4=0

a = 5; b = 1; c = -0.4;
Δ = b2-4ac
Δ = 12-4·5·(-0.4)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3}{2*5}=\frac{-4}{10}
=-2/5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3}{2*5}=\frac{2}{10}
=1/5
$