8/5y-4=1/4y-7

Solution for 8/5y-4=1/4y-7 equation:

8/5y-4=1/4y-7

We move all terms to the left:

8/5y-4-(1/4y-7)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 4y-7)!=0

y∈R


We get rid of parentheses

8/5y-1/4y+7-4=0

We calculate fractions


32y/20y^2+(-5y)/20y^2+7-4=0

We add all the numbers together, and all the variables

32y/20y^2+(-5y)/20y^2+3=0

We multiply all the terms by the denominator


32y+(-5y)+3*20y^2=0

Wy multiply elements

60y^2+32y+(-5y)=0

We get rid of parentheses

60y^2+32y-5y=0

We add all the numbers together, and all the variables

60y^2+27y=0

a = 60; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·60·0
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*60}=\frac{-54}{120}
=-9/20
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*60}=\frac{0}{120}
=0
$