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

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

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

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 3y-6)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


126y^2/96y^2+(-240y)/96y^2+224y/96y^2+6=0

We multiply all the terms by the denominator


126y^2+(-240y)+224y+6*96y^2=0

We add all the numbers together, and all the variables

126y^2+224y+(-240y)+6*96y^2=0

Wy multiply elements

126y^2+576y^2+224y+(-240y)=0

We get rid of parentheses

126y^2+576y^2+224y-240y=0

We add all the numbers together, and all the variables

702y^2-16y=0

a = 702; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·702·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*702}=\frac{0}{1404}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*702}=\frac{32}{1404}
=8/351
$