-1/3y-7/3=1/4y-1

Solution for -1/3y-7/3=1/4y-1 equation:

-1/3y-7/3=1/4y-1

We move all terms to the left:

-1/3y-7/3-(1/4y-1)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 4y-1)!=0

y∈R


We get rid of parentheses

-1/3y-1/4y+1-7/3=0

We calculate fractions


(-4y)/108y^2+(-27y)/108y^2+(-28y)/108y^2+1=0

We multiply all the terms by the denominator


(-4y)+(-27y)+(-28y)+1*108y^2=0

Wy multiply elements

108y^2+(-4y)+(-27y)+(-28y)=0

We get rid of parentheses

108y^2-4y-27y-28y=0

We add all the numbers together, and all the variables

108y^2-59y=0

a = 108; b = -59; c = 0;
Δ = b2-4ac
Δ = -592-4·108·0
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-59}{2*108}=\frac{0}{216}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+59}{2*108}=\frac{118}{216}
=59/108
$