-7/2w+3/2=-4/3w-7

Solution for -7/2w+3/2=-4/3w-7 equation:

-7/2w+3/2=-4/3w-7

We move all terms to the left:

-7/2w+3/2-(-4/3w-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

-7/2w+4/3w+7+3/2=0

We calculate fractions


(-21w)/24w^2+32w/24w^2+9w/24w^2+7=0

We multiply all the terms by the denominator


(-21w)+32w+9w+7*24w^2=0

We add all the numbers together, and all the variables

41w+(-21w)+7*24w^2=0

Wy multiply elements

168w^2+41w+(-21w)=0

We get rid of parentheses

168w^2+41w-21w=0

We add all the numbers together, and all the variables

168w^2+20w=0

a = 168; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·168·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*168}=\frac{-40}{336}
=-5/42
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*168}=\frac{0}{336}
=0
$