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

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

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

We move all terms to the left:

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


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


3w/24w^2+16w/24w^2+(-3w)/24w^2+4=0

We multiply all the terms by the denominator


3w+16w+(-3w)+4*24w^2=0

We add all the numbers together, and all the variables

19w+(-3w)+4*24w^2=0

Wy multiply elements

96w^2+19w+(-3w)=0

We get rid of parentheses

96w^2+19w-3w=0

We add all the numbers together, and all the variables

96w^2+16w=0

a = 96; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·96·0
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*96}=\frac{-32}{192}
=-1/6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*96}=\frac{0}{192}
=0
$