k+(6/k)=5

Solution for k+(6/k)=5 equation:

k+(6/k)=5

We move all terms to the left:

k+(6/k)-(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

k+(+6/k)-5=0

We get rid of parentheses

k+6/k-5=0

We multiply all the terms by the denominator


k*k-5*k+6=0

We add all the numbers together, and all the variables

-5k+k*k+6=0

Wy multiply elements

k^2-5k+6=0

a = 1; b = -5; c = +6;
Δ = b2-4ac
Δ = -52-4·1·6
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-1}{2*1}=\frac{4}{2}
=2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2*1}=\frac{6}{2}
=3
$