5/(2w)-7/(3w)=1

Solution for 5/(2w)-7/(3w)=1 equation:

5/(2w)-7/(3w)=1

We move all terms to the left:

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


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


We calculate fractions


15w/6w^2+(-14w)/6w^2-1=0

We multiply all the terms by the denominator


15w+(-14w)-1*6w^2=0

Wy multiply elements

-6w^2+15w+(-14w)=0

We get rid of parentheses

-6w^2+15w-14w=0

We add all the numbers together, and all the variables

-6w^2+w=0

a = -6; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-6)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-6}=\frac{-2}{-12}
=1/6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-6}=\frac{0}{-12}
=0
$