1/5y-8=2/3y+6

Solution for 1/5y-8=2/3y+6 equation:

1/5y-8=2/3y+6

We move all terms to the left:

1/5y-8-(2/3y+6)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 3y+6)!=0

y∈R


We get rid of parentheses

1/5y-2/3y-6-8=0

We calculate fractions


3y/15y^2+(-10y)/15y^2-6-8=0

We add all the numbers together, and all the variables

3y/15y^2+(-10y)/15y^2-14=0

We multiply all the terms by the denominator


3y+(-10y)-14*15y^2=0

Wy multiply elements

-210y^2+3y+(-10y)=0

We get rid of parentheses

-210y^2+3y-10y=0

We add all the numbers together, and all the variables

-210y^2-7y=0

a = -210; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-210)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-210}=\frac{0}{-420}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-210}=\frac{14}{-420}
=-1/30
$