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

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

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

We move all terms to the left:

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

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

We get rid of parentheses

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

We calculate fractions


(-6k)/1029k^2+(-2744k)/1029k^2+(-15k)/1029k^2-3=0

We multiply all the terms by the denominator


(-6k)+(-2744k)+(-15k)-3*1029k^2=0

Wy multiply elements

-3087k^2+(-6k)+(-2744k)+(-15k)=0

We get rid of parentheses

-3087k^2-6k-2744k-15k=0

We add all the numbers together, and all the variables

-3087k^2-2765k=0

a = -3087; b = -2765; c = 0;
Δ = b2-4ac
Δ = -27652-4·(-3087)·0
Δ = 7645225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7645225}=2765$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2765)-2765}{2*-3087}=\frac{0}{-6174}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2765)+2765}{2*-3087}=\frac{5530}{-6174}
=-395/441
$