7/3y+5=5/6y-4

Solution for 7/3y+5=5/6y-4 equation:

7/3y+5=5/6y-4

We move all terms to the left:

7/3y+5-(5/6y-4)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 6y-4)!=0

y∈R


We get rid of parentheses

7/3y-5/6y+4+5=0

We calculate fractions


42y/18y^2+(-15y)/18y^2+4+5=0

We add all the numbers together, and all the variables

42y/18y^2+(-15y)/18y^2+9=0

We multiply all the terms by the denominator


42y+(-15y)+9*18y^2=0

Wy multiply elements

162y^2+42y+(-15y)=0

We get rid of parentheses

162y^2+42y-15y=0

We add all the numbers together, and all the variables

162y^2+27y=0

a = 162; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·162·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*162}=\frac{-54}{324}
=-1/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*162}=\frac{0}{324}
=0
$