5/2y+17=2/3y-21

Solution for 5/2y+17=2/3y-21 equation:

5/2y+17=2/3y-21

We move all terms to the left:

5/2y+17-(2/3y-21)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 3y-21)!=0

y∈R


We get rid of parentheses

5/2y-2/3y+21+17=0

We calculate fractions


15y/6y^2+(-4y)/6y^2+21+17=0

We add all the numbers together, and all the variables

15y/6y^2+(-4y)/6y^2+38=0

We multiply all the terms by the denominator


15y+(-4y)+38*6y^2=0

Wy multiply elements

228y^2+15y+(-4y)=0

We get rid of parentheses

228y^2+15y-4y=0

We add all the numbers together, and all the variables

228y^2+11y=0

a = 228; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·228·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*228}=\frac{-22}{456}
=-11/228
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*228}=\frac{0}{456}
=0
$