38+7k=8/k+4

Solution for 38+7k=8/k+4 equation:

38+7k=8/k+4

We move all terms to the left:

38+7k-(8/k+4)=0


Domain of the equation: k+4)!=0

k∈R


We get rid of parentheses

7k-8/k-4+38=0

We multiply all the terms by the denominator


7k*k-4*k+38*k-8=0

We add all the numbers together, and all the variables

34k+7k*k-8=0

Wy multiply elements

7k^2+34k-8=0

a = 7; b = 34; c = -8;
Δ = b2-4ac
Δ = 342-4·7·(-8)
Δ = 1380
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:

$\sqrt{\Delta}=\sqrt{1380}=\sqrt{4*345}=\sqrt{4}*\sqrt{345}=2\sqrt{345}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{345}}{2*7}=\frac{-34-2\sqrt{345}}{14}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{345}}{2*7}=\frac{-34+2\sqrt{345}}{14}
$