5/7k-9=2k/3k-21

Solution for 5/7k-9=2k/3k-21 equation:

5/7k-9=2k/3k-21

We move all terms to the left:

5/7k-9-(2k/3k-21)=0


Domain of the equation: 7k!=0

k!=0/7

k!=0

k∈R



Domain of the equation: 3k-21)!=0

k∈R


We get rid of parentheses

5/7k-2k/3k+21-9=0

We calculate fractions


(-14k^2)/21k^2+15k/21k^2+21-9=0

We add all the numbers together, and all the variables

(-14k^2)/21k^2+15k/21k^2+12=0

We multiply all the terms by the denominator


(-14k^2)+15k+12*21k^2=0

Wy multiply elements

(-14k^2)+252k^2+15k=0

We get rid of parentheses

-14k^2+252k^2+15k=0

We add all the numbers together, and all the variables

238k^2+15k=0

a = 238; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·238·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*238}=\frac{-30}{476}
=-15/238
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*238}=\frac{0}{476}
=0
$