4/3y-5=7/6y-2

Solution for 4/3y-5=7/6y-2 equation:

4/3y-5=7/6y-2

We move all terms to the left:

4/3y-5-(7/6y-2)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 6y-2)!=0

y∈R


We get rid of parentheses

4/3y-7/6y+2-5=0

We calculate fractions


24y/18y^2+(-21y)/18y^2+2-5=0

We add all the numbers together, and all the variables

24y/18y^2+(-21y)/18y^2-3=0

We multiply all the terms by the denominator


24y+(-21y)-3*18y^2=0

Wy multiply elements

-54y^2+24y+(-21y)=0

We get rid of parentheses

-54y^2+24y-21y=0

We add all the numbers together, and all the variables

-54y^2+3y=0

a = -54; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-54)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-54}=\frac{-6}{-108}
=1/18
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-54}=\frac{0}{-108}
=0
$