-7/5k+6/7=8+5/7k

Solution for -7/5k+6/7=8+5/7k equation:

-7/5k+6/7=8+5/7k

We move all terms to the left:

-7/5k+6/7-(8+5/7k)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 7k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

-7/5k-(5/7k+8)+6/7=0

We get rid of parentheses

-7/5k-5/7k-8+6/7=0

We calculate fractions


(-2401k)/1715k^2+(-25k)/1715k^2+30k/1715k^2-8=0

We multiply all the terms by the denominator


(-2401k)+(-25k)+30k-8*1715k^2=0

We add all the numbers together, and all the variables

30k+(-2401k)+(-25k)-8*1715k^2=0

Wy multiply elements

-13720k^2+30k+(-2401k)+(-25k)=0

We get rid of parentheses

-13720k^2+30k-2401k-25k=0

We add all the numbers together, and all the variables

-13720k^2-2396k=0

a = -13720; b = -2396; c = 0;
Δ = b2-4ac
Δ = -23962-4·(-13720)·0
Δ = 5740816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5740816}=2396$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2396)-2396}{2*-13720}=\frac{0}{-27440}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2396)+2396}{2*-13720}=\frac{4792}{-27440}
=-599/3430
$