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

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

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

We move all terms to the left:

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


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 4y-3)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


(-336y^2)/48y^2+112y/48y^2+60y/48y^2+3=0

We multiply all the terms by the denominator


(-336y^2)+112y+60y+3*48y^2=0

We add all the numbers together, and all the variables

(-336y^2)+172y+3*48y^2=0

Wy multiply elements

(-336y^2)+144y^2+172y=0

We get rid of parentheses

-336y^2+144y^2+172y=0

We add all the numbers together, and all the variables

-192y^2+172y=0

a = -192; b = 172; c = 0;
Δ = b2-4ac
Δ = 1722-4·(-192)·0
Δ = 29584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{29584}=172$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(172)-172}{2*-192}=\frac{-344}{-384}
=43/48
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(172)+172}{2*-192}=\frac{0}{-384}
=0
$