1/2*k+1/5*k=1

Solution for 1/2*k+1/5*k=1 equation:

1/2k+1/5k=1

We move all terms to the left:

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


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R


We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

7k-1*10k^2=0

Wy multiply elements

-10k^2+7k=0

a = -10; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-10)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-10}=\frac{-14}{-20}
=7/10
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-10}=\frac{0}{-20}
=0
$