5/3k+6=7/2k-3

Solution for 5/3k+6=7/2k-3 equation:

5/3k+6=7/2k-3

We move all terms to the left:

5/3k+6-(7/2k-3)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R



Domain of the equation: 2k-3)!=0

k∈R


We get rid of parentheses

5/3k-7/2k+3+6=0

We calculate fractions


10k/6k^2+(-21k)/6k^2+3+6=0

We add all the numbers together, and all the variables

10k/6k^2+(-21k)/6k^2+9=0

We multiply all the terms by the denominator


10k+(-21k)+9*6k^2=0

Wy multiply elements

54k^2+10k+(-21k)=0

We get rid of parentheses

54k^2+10k-21k=0

We add all the numbers together, and all the variables

54k^2-11k=0

a = 54; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·54·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*54}=\frac{0}{108}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*54}=\frac{22}{108}
=11/54
$