9/7k+5/8=2-7/3k

Solution for 9/7k+5/8=2-7/3k equation:

9/7k+5/8=2-7/3k

We move all terms to the left:

9/7k+5/8-(2-7/3k)=0


Domain of the equation: 7k!=0

k!=0/7

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

9/7k-(-7/3k+2)+5/8=0

We get rid of parentheses

9/7k+7/3k-2+5/8=0

We calculate fractions


315k^2/1344k^2+1728k/1344k^2+3136k/1344k^2-2=0

We multiply all the terms by the denominator


315k^2+1728k+3136k-2*1344k^2=0

We add all the numbers together, and all the variables

315k^2+4864k-2*1344k^2=0

Wy multiply elements

315k^2-2688k^2+4864k=0

We add all the numbers together, and all the variables

-2373k^2+4864k=0

a = -2373; b = 4864; c = 0;
Δ = b2-4ac
Δ = 48642-4·(-2373)·0
Δ = 23658496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{23658496}=4864$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4864)-4864}{2*-2373}=\frac{-9728}{-4746}
=2+118/2373
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4864)+4864}{2*-2373}=\frac{0}{-4746}
=0
$