-8/5k+6/7=3+7/3k

Solution for -8/5k+6/7=3+7/3k equation:

-8/5k+6/7=3+7/3k

We move all terms to the left:

-8/5k+6/7-(3+7/3k)=0


Domain of the equation: 5k!=0

k!=0/5

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

-8/5k-(7/3k+3)+6/7=0

We get rid of parentheses

-8/5k-7/3k-3+6/7=0

We calculate fractions


270k^2/735k^2+(-1176k)/735k^2+(-1715k)/735k^2-3=0

We multiply all the terms by the denominator


270k^2+(-1176k)+(-1715k)-3*735k^2=0

Wy multiply elements

270k^2-2205k^2+(-1176k)+(-1715k)=0

We get rid of parentheses

270k^2-2205k^2-1176k-1715k=0

We add all the numbers together, and all the variables

-1935k^2-2891k=0

a = -1935; b = -2891; c = 0;
Δ = b2-4ac
Δ = -28912-4·(-1935)·0
Δ = 8357881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8357881}=2891$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2891)-2891}{2*-1935}=\frac{0}{-3870}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2891)+2891}{2*-1935}=\frac{5782}{-3870}
=-1+956/1935
$