3/7k+5/2=7-8/5k

Solution for 3/7k+5/2=7-8/5k equation:

3/7k+5/2=7-8/5k

We move all terms to the left:

3/7k+5/2-(7-8/5k)=0


Domain of the equation: 7k!=0

k!=0/7

k!=0

k∈R



Domain of the equation: 5k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

3/7k-(-8/5k+7)+5/2=0

We get rid of parentheses

3/7k+8/5k-7+5/2=0

We calculate fractions


875k^2/140k^2+60k/140k^2+224k/140k^2-7=0

We multiply all the terms by the denominator


875k^2+60k+224k-7*140k^2=0

We add all the numbers together, and all the variables

875k^2+284k-7*140k^2=0

Wy multiply elements

875k^2-980k^2+284k=0

We add all the numbers together, and all the variables

-105k^2+284k=0

a = -105; b = 284; c = 0;
Δ = b2-4ac
Δ = 2842-4·(-105)·0
Δ = 80656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{80656}=284$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(284)-284}{2*-105}=\frac{-568}{-210}
=2+74/105
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(284)+284}{2*-105}=\frac{0}{-210}
=0
$