7=6k-14/k

Solution for 7=6k-14/k equation:

7=6k-14/k

We move all terms to the left:

7-(6k-14/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

-(+6k-14/k)+7=0

We get rid of parentheses

-6k+14/k+7=0

We multiply all the terms by the denominator


-6k*k+7*k+14=0

We add all the numbers together, and all the variables

7k-6k*k+14=0

Wy multiply elements

-6k^2+7k+14=0

a = -6; b = 7; c = +14;
Δ = b2-4ac
Δ = 72-4·(-6)·14
Δ = 385
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{385}}{2*-6}=\frac{-7-\sqrt{385}}{-12}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{385}}{2*-6}=\frac{-7+\sqrt{385}}{-12}
$