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

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

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

We move all terms to the left:

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

We calculate fractions


135y/54y^2+10y/54y^2+(-14y)/54y^2+6=0

We multiply all the terms by the denominator


135y+10y+(-14y)+6*54y^2=0

We add all the numbers together, and all the variables

145y+(-14y)+6*54y^2=0

Wy multiply elements

324y^2+145y+(-14y)=0

We get rid of parentheses

324y^2+145y-14y=0

We add all the numbers together, and all the variables

324y^2+131y=0

a = 324; b = 131; c = 0;
Δ = b2-4ac
Δ = 1312-4·324·0
Δ = 17161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17161}=131$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(131)-131}{2*324}=\frac{-262}{648}
=-131/324
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(131)+131}{2*324}=\frac{0}{648}
=0
$