1/5k-3=5/3k+7

Solution for 1/5k-3=5/3k+7 equation:

1/5k-3=5/3k+7

We move all terms to the left:

1/5k-3-(5/3k+7)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 3k+7)!=0

k∈R


We get rid of parentheses

1/5k-5/3k-7-3=0

We calculate fractions


3k/15k^2+(-25k)/15k^2-7-3=0

We add all the numbers together, and all the variables

3k/15k^2+(-25k)/15k^2-10=0

We multiply all the terms by the denominator


3k+(-25k)-10*15k^2=0

Wy multiply elements

-150k^2+3k+(-25k)=0

We get rid of parentheses

-150k^2+3k-25k=0

We add all the numbers together, and all the variables

-150k^2-22k=0

a = -150; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·(-150)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*-150}=\frac{0}{-300}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*-150}=\frac{44}{-300}
=-11/75
$