4/w-12=2/3w

Solution for 4/w-12=2/3w equation:

4/w-12=2/3w

We move all terms to the left:

4/w-12-(2/3w)=0


Domain of the equation: w!=0

w∈R



Domain of the equation: 3w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

4/w-(+2/3w)-12=0

We get rid of parentheses

4/w-2/3w-12=0

We calculate fractions


12w/3w^2+(-2w)/3w^2-12=0

We multiply all the terms by the denominator


12w+(-2w)-12*3w^2=0

Wy multiply elements

-36w^2+12w+(-2w)=0

We get rid of parentheses

-36w^2+12w-2w=0

We add all the numbers together, and all the variables

-36w^2+10w=0

a = -36; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-36)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-36}=\frac{-20}{-72}
=5/18
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-36}=\frac{0}{-72}
=0
$