-2/3w-2=5-1/4w

Solution for -2/3w-2=5-1/4w equation:

-2/3w-2=5-1/4w

We move all terms to the left:

-2/3w-2-(5-1/4w)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 4w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

-2/3w-(-1/4w+5)-2=0

We get rid of parentheses

-2/3w+1/4w-5-2=0

We calculate fractions


(-8w)/12w^2+3w/12w^2-5-2=0

We add all the numbers together, and all the variables

(-8w)/12w^2+3w/12w^2-7=0

We multiply all the terms by the denominator


(-8w)+3w-7*12w^2=0

We add all the numbers together, and all the variables

3w+(-8w)-7*12w^2=0

Wy multiply elements

-84w^2+3w+(-8w)=0

We get rid of parentheses

-84w^2+3w-8w=0

We add all the numbers together, and all the variables

-84w^2-5w=0

a = -84; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-84)·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*-84}=\frac{0}{-168}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-84}=\frac{10}{-168}
=-5/84
$