-5/3y-7/3=7/5y-6

Solution for -5/3y-7/3=7/5y-6 equation:

-5/3y-7/3=7/5y-6

We move all terms to the left:

-5/3y-7/3-(7/5y-6)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 5y-6)!=0

y∈R


We get rid of parentheses

-5/3y-7/5y+6-7/3=0

We calculate fractions


(-25y)/135y^2+(-189y)/135y^2+(-35y)/135y^2+6=0

We multiply all the terms by the denominator


(-25y)+(-189y)+(-35y)+6*135y^2=0

Wy multiply elements

810y^2+(-25y)+(-189y)+(-35y)=0

We get rid of parentheses

810y^2-25y-189y-35y=0

We add all the numbers together, and all the variables

810y^2-249y=0

a = 810; b = -249; c = 0;
Δ = b2-4ac
Δ = -2492-4·810·0
Δ = 62001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{62001}=249$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-249)-249}{2*810}=\frac{0}{1620}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-249)+249}{2*810}=\frac{498}{1620}
=83/270
$