(1/w-2)-(2/3w-6)=1/3w-6

Solution for (1/w-2)-(2/3w-6)=1/3w-6 equation:

(1/w-2)-(2/3w-6)=1/3w-6

We move all terms to the left:

(1/w-2)-(2/3w-6)-(1/3w-6)=0


Domain of the equation: w-2)!=0

w∈R



Domain of the equation: 3w-6)!=0

w∈R


We get rid of parentheses

1/w-2/3w-1/3w-2+6+6=0

We calculate fractions


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

We add all the numbers together, and all the variables

3w/3w^2+(-1w-2)/3w^2+10=0

We multiply all the terms by the denominator


3w+(-1w-2)+10*3w^2=0

Wy multiply elements

30w^2+3w+(-1w-2)=0

We get rid of parentheses

30w^2+3w-1w-2=0

We add all the numbers together, and all the variables

30w^2+2w-2=0

a = 30; b = 2; c = -2;
Δ = b2-4ac
Δ = 22-4·30·(-2)
Δ = 244
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{61}}{2*30}=\frac{-2-2\sqrt{61}}{60}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{61}}{2*30}=\frac{-2+2\sqrt{61}}{60}
$