7/5w-3/2w=1

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

7/5w-3/2w=1

We move all terms to the left:

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


Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R



Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R


We calculate fractions


14w/10w^2+(-15w)/10w^2-1=0

We multiply all the terms by the denominator


14w+(-15w)-1*10w^2=0

Wy multiply elements

-10w^2+14w+(-15w)=0

We get rid of parentheses

-10w^2+14w-15w=0

We add all the numbers together, and all the variables

-10w^2-1w=0

a = -10; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-10)·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*-10}=\frac{0}{-20}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-10}=\frac{2}{-20}
=-1/10
$