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

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

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

We move all terms to the left:

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


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R



Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We get rid of parentheses

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

We calculate fractions


315y^2/84y^2+24y/84y^2+(-140y)/84y^2=0

We multiply all the terms by the denominator


315y^2+24y+(-140y)=0

We get rid of parentheses

315y^2+24y-140y=0

We add all the numbers together, and all the variables

315y^2-116y=0

a = 315; b = -116; c = 0;
Δ = b2-4ac
Δ = -1162-4·315·0
Δ = 13456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13456}=116$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-116)-116}{2*315}=\frac{0}{630}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+116}{2*315}=\frac{232}{630}
=116/315
$