-10+1/5k=k+2

Solution for -10+1/5k=k+2 equation:

-10+1/5k=k+2

We move all terms to the left:

-10+1/5k-(k+2)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R


We get rid of parentheses

1/5k-k-2-10=0

We multiply all the terms by the denominator


-k*5k-2*5k-10*5k+1=0

Wy multiply elements

-5k^2-10k-50k+1=0

We add all the numbers together, and all the variables

-5k^2-60k+1=0

a = -5; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·(-5)·1
Δ = 3620
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3620}=\sqrt{4*905}=\sqrt{4}*\sqrt{905}=2\sqrt{905}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{905}}{2*-5}=\frac{60-2\sqrt{905}}{-10}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{905}}{2*-5}=\frac{60+2\sqrt{905}}{-10}
$