(-8/k)+4k=5

Solution for (-8/k)+4k=5 equation:

(-8/k)+4k=5

We move all terms to the left:

(-8/k)+4k-(5)=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+(-8/k)-5=0

We get rid of parentheses

4k-8/k-5=0

We multiply all the terms by the denominator


4k*k-5*k-8=0

We add all the numbers together, and all the variables

-5k+4k*k-8=0

Wy multiply elements

4k^2-5k-8=0

a = 4; b = -5; c = -8;
Δ = b2-4ac
Δ = -52-4·4·(-8)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{17}}{2*4}=\frac{5-3\sqrt{17}}{8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{17}}{2*4}=\frac{5+3\sqrt{17}}{8}
$