3/4k-2/2=5/6k

Solution for 3/4k-2/2=5/6k equation:

3/4k-2/2=5/6k

We move all terms to the left:

3/4k-2/2-(5/6k)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R



Domain of the equation: 6k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

3/4k-(+5/6k)-2/2=0

We add all the numbers together, and all the variables

3/4k-(+5/6k)-1=0

We get rid of parentheses

3/4k-5/6k-1=0

We calculate fractions


18k/24k^2+(-20k)/24k^2-1=0

We multiply all the terms by the denominator


18k+(-20k)-1*24k^2=0

Wy multiply elements

-24k^2+18k+(-20k)=0

We get rid of parentheses

-24k^2+18k-20k=0

We add all the numbers together, and all the variables

-24k^2-2k=0

a = -24; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-24)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-24}=\frac{0}{-48}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-24}=\frac{4}{-48}
=-1/12
$