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

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

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

We move all terms to the left:

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


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



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

w∈R


We get rid of parentheses

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

We calculate fractions


(-56w)/24w^2+3w/24w^2+9w/24w^2+2=0

We multiply all the terms by the denominator


(-56w)+3w+9w+2*24w^2=0

We add all the numbers together, and all the variables

12w+(-56w)+2*24w^2=0

Wy multiply elements

48w^2+12w+(-56w)=0

We get rid of parentheses

48w^2+12w-56w=0

We add all the numbers together, and all the variables

48w^2-44w=0

a = 48; b = -44; c = 0;
Δ = b2-4ac
Δ = -442-4·48·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-44}{2*48}=\frac{0}{96}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+44}{2*48}=\frac{88}{96}
=11/12
$