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

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

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

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 3y-7)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


189y/108y^2+(-16y)/108y^2+(-20y)/108y^2+7=0

We multiply all the terms by the denominator


189y+(-16y)+(-20y)+7*108y^2=0

Wy multiply elements

756y^2+189y+(-16y)+(-20y)=0

We get rid of parentheses

756y^2+189y-16y-20y=0

We add all the numbers together, and all the variables

756y^2+153y=0

a = 756; b = 153; c = 0;
Δ = b2-4ac
Δ = 1532-4·756·0
Δ = 23409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{23409}=153$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(153)-153}{2*756}=\frac{-306}{1512}
=-17/84
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(153)+153}{2*756}=\frac{0}{1512}
=0
$