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

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

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

We move all terms to the left:

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


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 3y-2)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


135y^2/375y^2+(-300y)/375y^2+875y/375y^2+2=0

We multiply all the terms by the denominator


135y^2+(-300y)+875y+2*375y^2=0

We add all the numbers together, and all the variables

135y^2+875y+(-300y)+2*375y^2=0

Wy multiply elements

135y^2+750y^2+875y+(-300y)=0

We get rid of parentheses

135y^2+750y^2+875y-300y=0

We add all the numbers together, and all the variables

885y^2+575y=0

a = 885; b = 575; c = 0;
Δ = b2-4ac
Δ = 5752-4·885·0
Δ = 330625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{330625}=575$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(575)-575}{2*885}=\frac{-1150}{1770}
=-115/177
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(575)+575}{2*885}=\frac{0}{1770}
=0
$