3/4w-4/8=3/2w+4

Solution for 3/4w-4/8=3/2w+4 equation:

3/4w-4/8=3/2w+4

We move all terms to the left:

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


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 2w+4)!=0

w∈R


We get rid of parentheses

3/4w-3/2w-4-4/8=0

We calculate fractions


(-64w^2)/512w^2+384w/512w^2+(-768w)/512w^2-4=0

We multiply all the terms by the denominator


(-64w^2)+384w+(-768w)-4*512w^2=0

Wy multiply elements

(-64w^2)-2048w^2+384w+(-768w)=0

We get rid of parentheses

-64w^2-2048w^2+384w-768w=0

We add all the numbers together, and all the variables

-2112w^2-384w=0

a = -2112; b = -384; c = 0;
Δ = b2-4ac
Δ = -3842-4·(-2112)·0
Δ = 147456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{147456}=384$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-384)-384}{2*-2112}=\frac{0}{-4224}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-384)+384}{2*-2112}=\frac{768}{-4224}
=-2/11
$