10k2-10k+2=-k

Solution for 10k2-10k+2=-k equation:

10k^2-10k+2=-k

We move all terms to the left:

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

We add all the numbers together, and all the variables

10k^2-10k-(-1k)+2=0

We get rid of parentheses

10k^2-10k+1k+2=0

We add all the numbers together, and all the variables

10k^2-9k+2=0

a = 10; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·10·2
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-1}{2*10}=\frac{8}{20}
=2/5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+1}{2*10}=\frac{10}{20}
=1/2
$