2/5y-7=1/3y+8

Solution for 2/5y-7=1/3y+8 equation:

2/5y-7=1/3y+8

We move all terms to the left:

2/5y-7-(1/3y+8)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 3y+8)!=0

y∈R


We get rid of parentheses

2/5y-1/3y-8-7=0

We calculate fractions


6y/15y^2+(-5y)/15y^2-8-7=0

We add all the numbers together, and all the variables

6y/15y^2+(-5y)/15y^2-15=0

We multiply all the terms by the denominator


6y+(-5y)-15*15y^2=0

Wy multiply elements

-225y^2+6y+(-5y)=0

We get rid of parentheses

-225y^2+6y-5y=0

We add all the numbers together, and all the variables

-225y^2+y=0

a = -225; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-225)·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*-225}=\frac{-2}{-450}
=1/225
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-225}=\frac{0}{-450}
=0
$