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

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

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

We move all terms to the left:

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


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 3y+4)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


12y/15y^2+(-10y)/15y^2-4-3=0

We add all the numbers together, and all the variables

12y/15y^2+(-10y)/15y^2-7=0

We multiply all the terms by the denominator


12y+(-10y)-7*15y^2=0

Wy multiply elements

-105y^2+12y+(-10y)=0

We get rid of parentheses

-105y^2+12y-10y=0

We add all the numbers together, and all the variables

-105y^2+2y=0

a = -105; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-105)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-105}=\frac{-4}{-210}
=2/105
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-105}=\frac{0}{-210}
=0
$