10k^2+3k=k

Solution for 10k^2+3k=k equation:

10k^2+3k=k

We move all terms to the left:

10k^2+3k-(k)=0

We add all the numbers together, and all the variables

10k^2+2k=0

a = 10; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·10·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*10}=\frac{-4}{20}
=-1/5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*10}=\frac{0}{20}
=0
$