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

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

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

We move all terms to the left:

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


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 3w-5)!=0

w∈R


We get rid of parentheses

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

We calculate fractions


3w/6w^2+(-4w)/6w^2+5+3=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

48w^2+3w+(-4w)=0

We get rid of parentheses

48w^2+3w-4w=0

We add all the numbers together, and all the variables

48w^2-1w=0

a = 48; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·48·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*48}=\frac{0}{96}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*48}=\frac{2}{96}
=1/48
$