2/3w-4=1/4w+6

Solution for 2/3w-4=1/4w+6 equation:

2/3w-4=1/4w+6

We move all terms to the left:

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


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 4w+6)!=0

w∈R


We get rid of parentheses

2/3w-1/4w-6-4=0

We calculate fractions


8w/12w^2+(-3w)/12w^2-6-4=0

We add all the numbers together, and all the variables

8w/12w^2+(-3w)/12w^2-10=0

We multiply all the terms by the denominator


8w+(-3w)-10*12w^2=0

Wy multiply elements

-120w^2+8w+(-3w)=0

We get rid of parentheses

-120w^2+8w-3w=0

We add all the numbers together, and all the variables

-120w^2+5w=0

a = -120; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-120)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-120}=\frac{-10}{-240}
=1/24
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-120}=\frac{0}{-240}
=0
$