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

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

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

We move all terms to the left:

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


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 3w-2)!=0

w∈R


We get rid of parentheses

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

We calculate fractions


54w^2/96w^2+48w/96w^2+(-32w)/96w^2+2=0

We multiply all the terms by the denominator


54w^2+48w+(-32w)+2*96w^2=0

Wy multiply elements

54w^2+192w^2+48w+(-32w)=0

We get rid of parentheses

54w^2+192w^2+48w-32w=0

We add all the numbers together, and all the variables

246w^2+16w=0

a = 246; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·246·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*246}=\frac{-32}{492}
=-8/123
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*246}=\frac{0}{492}
=0
$