4/3w-2/w=1

Solution for 4/3w-2/w=1 equation:

4/3w-2/w=1

We move all terms to the left:

4/3w-2/w-(1)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: w!=0

w∈R


We calculate fractions


4w/3w^2+(-6w)/3w^2-1=0

We multiply all the terms by the denominator


4w+(-6w)-1*3w^2=0

Wy multiply elements

-3w^2+4w+(-6w)=0

We get rid of parentheses

-3w^2+4w-6w=0

We add all the numbers together, and all the variables

-3w^2-2w=0

a = -3; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-3)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-3}=\frac{0}{-6}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-3}=\frac{4}{-6}
=-2/3
$