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

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

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

We move all terms to the left:

-4/3y-7/2-(7/6y-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

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

We calculate fractions


(-756y^2)/72y^2+(-96y)/72y^2+(-84y)/72y^2+4=0

We multiply all the terms by the denominator


(-756y^2)+(-96y)+(-84y)+4*72y^2=0

Wy multiply elements

(-756y^2)+288y^2+(-96y)+(-84y)=0

We get rid of parentheses

-756y^2+288y^2-96y-84y=0

We add all the numbers together, and all the variables

-468y^2-180y=0

a = -468; b = -180; c = 0;
Δ = b2-4ac
Δ = -1802-4·(-468)·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-180}{2*-468}=\frac{0}{-936}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+180}{2*-468}=\frac{360}{-936}
=-5/13
$