3/k=11/2k-20

Solution for 3/k=11/2k-20 equation:

3/k=11/2k-20

We move all terms to the left:

3/k-(11/2k-20)=0


Domain of the equation: k!=0

k∈R



Domain of the equation: 2k-20)!=0

k∈R


We get rid of parentheses

3/k-11/2k+20=0

We calculate fractions


6k/2k^2+(-11k)/2k^2+20=0

We multiply all the terms by the denominator


6k+(-11k)+20*2k^2=0

Wy multiply elements

40k^2+6k+(-11k)=0

We get rid of parentheses

40k^2+6k-11k=0

We add all the numbers together, and all the variables

40k^2-5k=0

a = 40; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·40·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*40}=\frac{0}{80}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*40}=\frac{10}{80}
=1/8
$