7/3y-2/5y=1

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

7/3y-2/5y=1

We move all terms to the left:

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


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We calculate fractions


35y/15y^2+(-6y)/15y^2-1=0

We multiply all the terms by the denominator


35y+(-6y)-1*15y^2=0

Wy multiply elements

-15y^2+35y+(-6y)=0

We get rid of parentheses

-15y^2+35y-6y=0

We add all the numbers together, and all the variables

-15y^2+29y=0

a = -15; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-15)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-15}=\frac{-58}{-30}
=1+14/15
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-15}=\frac{0}{-30}
=0
$