7y/5y=y-4

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

7y/5y=y-4

We move all terms to the left:

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


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We get rid of parentheses

7y/5y-y+4=0

We multiply all the terms by the denominator


7y-y*5y+4*5y=0

Wy multiply elements

-5y^2+7y+20y=0

We add all the numbers together, and all the variables

-5y^2+27y=0

a = -5; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-5)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-5}=\frac{-54}{-10}
=5+2/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-5}=\frac{0}{-10}
=0
$