3/2k-2/3k=5/18

Solution for 3/2k-2/3k=5/18 equation:

3/2k-2/3k=5/18

We move all terms to the left:

3/2k-2/3k-(5/18)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R


We add all the numbers together, and all the variables

3/2k-2/3k-(+5/18)=0

We get rid of parentheses

3/2k-2/3k-5/18=0

We calculate fractions


(-90k^2)/108k^2+162k/108k^2+(-72k)/108k^2=0

We multiply all the terms by the denominator


(-90k^2)+162k+(-72k)=0

We get rid of parentheses

-90k^2+162k-72k=0

We add all the numbers together, and all the variables

-90k^2+90k=0

a = -90; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·(-90)·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90}{2*-90}=\frac{-180}{-180}
=1
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*-90}=\frac{0}{-180}
=0
$