18/4-2/5k=5-1/3k

Solution for 18/4-2/5k=5-1/3k equation:

18/4-2/5k=5-1/3k

We move all terms to the left:

18/4-2/5k-(5-1/3k)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 3k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

-2/5k-(-1/3k+5)+18/4=0

We get rid of parentheses

-2/5k+1/3k-5+18/4=0

We calculate fractions


810k^2/240k^2+(-96k)/240k^2+80k/240k^2-5=0

We multiply all the terms by the denominator


810k^2+(-96k)+80k-5*240k^2=0

We add all the numbers together, and all the variables

810k^2+80k+(-96k)-5*240k^2=0

Wy multiply elements

810k^2-1200k^2+80k+(-96k)=0

We get rid of parentheses

810k^2-1200k^2+80k-96k=0

We add all the numbers together, and all the variables

-390k^2-16k=0

a = -390; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-390)·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*-390}=\frac{0}{-780}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-390}=\frac{32}{-780}
=-8/195
$