3/5k+9/7=6+4/7k

Solution for 3/5k+9/7=6+4/7k equation:

3/5k+9/7=6+4/7k

We move all terms to the left:

3/5k+9/7-(6+4/7k)=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

3/5k-(4/7k+6)+9/7=0

We get rid of parentheses

3/5k-4/7k-6+9/7=0

We calculate fractions


1029k/1715k^2+(-20k)/1715k^2+45k/1715k^2-6=0

We multiply all the terms by the denominator


1029k+(-20k)+45k-6*1715k^2=0

We add all the numbers together, and all the variables

1074k+(-20k)-6*1715k^2=0

Wy multiply elements

-10290k^2+1074k+(-20k)=0

We get rid of parentheses

-10290k^2+1074k-20k=0

We add all the numbers together, and all the variables

-10290k^2+1054k=0

a = -10290; b = 1054; c = 0;
Δ = b2-4ac
Δ = 10542-4·(-10290)·0
Δ = 1110916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1110916}=1054$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1054)-1054}{2*-10290}=\frac{-2108}{-20580}
=527/5145
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1054)+1054}{2*-10290}=\frac{0}{-20580}
=0
$