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

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

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

We move all terms to the left:

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


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 3w-1)!=0

w∈R


We get rid of parentheses

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

We calculate fractions


189w/108w^2+20w/108w^2+(-28w)/108w^2+1=0

We multiply all the terms by the denominator


189w+20w+(-28w)+1*108w^2=0

We add all the numbers together, and all the variables

209w+(-28w)+1*108w^2=0

Wy multiply elements

108w^2+209w+(-28w)=0

We get rid of parentheses

108w^2+209w-28w=0

We add all the numbers together, and all the variables

108w^2+181w=0

a = 108; b = 181; c = 0;
Δ = b2-4ac
Δ = 1812-4·108·0
Δ = 32761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32761}=181$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(181)-181}{2*108}=\frac{-362}{216}
=-1+73/108
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(181)+181}{2*108}=\frac{0}{216}
=0
$