6/5k+2/k-3=0

Solution for 6/5k+2/k-3=0 equation:

6/5k+2/k-3=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: k!=0

k∈R


We calculate fractions


6k/5k^2+10k/5k^2-3=0

We multiply all the terms by the denominator


6k+10k-3*5k^2=0

We add all the numbers together, and all the variables

16k-3*5k^2=0

Wy multiply elements

-15k^2+16k=0

a = -15; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-15)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-15}=\frac{-32}{-30}
=1+1/15
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-15}=\frac{0}{-30}
=0
$