-1/2w+3=-1/3w+7

Solution for -1/2w+3=-1/3w+7 equation:

-1/2w+3=-1/3w+7

We move all terms to the left:

-1/2w+3-(-1/3w+7)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 3w+7)!=0

w∈R


We get rid of parentheses

-1/2w+1/3w-7+3=0

We calculate fractions


(-3w)/6w^2+2w/6w^2-7+3=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-24w^2+2w+(-3w)=0

We get rid of parentheses

-24w^2+2w-3w=0

We add all the numbers together, and all the variables

-24w^2-1w=0

a = -24; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-24)·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*-24}=\frac{0}{-48}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-24}=\frac{2}{-48}
=-1/24
$