10k(k+1)=k-2

Solution for 10k(k+1)=k-2 equation:

10k(k+1)=k-2

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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