-2/3w+5/2=-1/4w-7

Solution for -2/3w+5/2=-1/4w-7 equation:

-2/3w+5/2=-1/4w-7

We move all terms to the left:

-2/3w+5/2-(-1/4w-7)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 4w-7)!=0

w∈R


We get rid of parentheses

-2/3w+1/4w+7+5/2=0

We calculate fractions


240w^2/48w^2+(-32w)/48w^2+12w/48w^2+7=0

We multiply all the terms by the denominator


240w^2+(-32w)+12w+7*48w^2=0

We add all the numbers together, and all the variables

240w^2+12w+(-32w)+7*48w^2=0

Wy multiply elements

240w^2+336w^2+12w+(-32w)=0

We get rid of parentheses

240w^2+336w^2+12w-32w=0

We add all the numbers together, and all the variables

576w^2-20w=0

a = 576; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·576·0
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*576}=\frac{0}{1152}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*576}=\frac{40}{1152}
=5/144
$