-5/2y+3/5=-3/5y-6

Solution for -5/2y+3/5=-3/5y-6 equation:

-5/2y+3/5=-3/5y-6

We move all terms to the left:

-5/2y+3/5-(-3/5y-6)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



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

y∈R


We get rid of parentheses

-5/2y+3/5y+6+3/5=0

We calculate fractions


(-625y)/250y^2+6y/250y^2+6y/250y^2+6=0

We multiply all the terms by the denominator


(-625y)+6y+6y+6*250y^2=0

We add all the numbers together, and all the variables

12y+(-625y)+6*250y^2=0

Wy multiply elements

1500y^2+12y+(-625y)=0

We get rid of parentheses

1500y^2+12y-625y=0

We add all the numbers together, and all the variables

1500y^2-613y=0

a = 1500; b = -613; c = 0;
Δ = b2-4ac
Δ = -6132-4·1500·0
Δ = 375769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{375769}=613$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-613)-613}{2*1500}=\frac{0}{3000}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-613)+613}{2*1500}=\frac{1226}{3000}
=613/1500
$