7/5y-2=5/4y

Solution for 7/5y-2=5/4y equation:

7/5y-2=5/4y

We move all terms to the left:

7/5y-2-(5/4y)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 4y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

7/5y-(+5/4y)-2=0

We get rid of parentheses

7/5y-5/4y-2=0

We calculate fractions


28y/20y^2+(-25y)/20y^2-2=0

We multiply all the terms by the denominator


28y+(-25y)-2*20y^2=0

Wy multiply elements

-40y^2+28y+(-25y)=0

We get rid of parentheses

-40y^2+28y-25y=0

We add all the numbers together, and all the variables

-40y^2+3y=0

a = -40; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-40)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-40}=\frac{-6}{-80}
=3/40
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-40}=\frac{0}{-80}
=0
$