4/7y=3/5y-2

Solution for 4/7y=3/5y-2 equation:

4/7y=3/5y-2

We move all terms to the left:

4/7y-(3/5y-2)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R



Domain of the equation: 5y-2)!=0

y∈R


We get rid of parentheses

4/7y-3/5y+2=0

We calculate fractions


20y/35y^2+(-21y)/35y^2+2=0

We multiply all the terms by the denominator


20y+(-21y)+2*35y^2=0

Wy multiply elements

70y^2+20y+(-21y)=0

We get rid of parentheses

70y^2+20y-21y=0

We add all the numbers together, and all the variables

70y^2-1y=0

a = 70; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·70·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*70}=\frac{0}{140}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*70}=\frac{2}{140}
=1/70
$