-7/6k+3/7=6+6/5k

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

-7/6k+3/7=6+6/5k

We move all terms to the left:

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


Domain of the equation: 6k!=0

k!=0/6

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

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

We get rid of parentheses

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

We calculate fractions


450k^2/1470k^2+(-1715k)/1470k^2+(-1764k)/1470k^2-6=0

We multiply all the terms by the denominator


450k^2+(-1715k)+(-1764k)-6*1470k^2=0

Wy multiply elements

450k^2-8820k^2+(-1715k)+(-1764k)=0

We get rid of parentheses

450k^2-8820k^2-1715k-1764k=0

We add all the numbers together, and all the variables

-8370k^2-3479k=0

a = -8370; b = -3479; c = 0;
Δ = b2-4ac
Δ = -34792-4·(-8370)·0
Δ = 12103441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12103441}=3479$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3479)-3479}{2*-8370}=\frac{0}{-16740}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3479)+3479}{2*-8370}=\frac{6958}{-16740}
=-3479/8370
$