4k+7=7k-1/k=4

Solution for 4k+7=7k-1/k=4 equation:

4k+7=7k-1/k=4

We move all terms to the left:

4k+7-(7k-1/k)=0


Domain of the equation: k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

4k-(+7k-1/k)+7=0

We get rid of parentheses

4k-7k+1/k+7=0

We multiply all the terms by the denominator


4k*k-7k*k+7*k+1=0

We add all the numbers together, and all the variables

7k+4k*k-7k*k+1=0

Wy multiply elements

4k^2-7k^2+7k+1=0

We add all the numbers together, and all the variables

-3k^2+7k+1=0

a = -3; b = 7; c = +1;
Δ = b2-4ac
Δ = 72-4·(-3)·1
Δ = 61
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{61}}{2*-3}=\frac{-7-\sqrt{61}}{-6}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{61}}{2*-3}=\frac{-7+\sqrt{61}}{-6}
$