21/2y=10-12/3y

Solution for 21/2y=10-12/3y equation:

21/2y=10-12/3y

We move all terms to the left:

21/2y-(10-12/3y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 3y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

21/2y-(-12/3y+10)=0

We get rid of parentheses

21/2y+12/3y-10=0

We calculate fractions


63y/6y^2+24y/6y^2-10=0

We multiply all the terms by the denominator


63y+24y-10*6y^2=0

We add all the numbers together, and all the variables

87y-10*6y^2=0

Wy multiply elements

-60y^2+87y=0

a = -60; b = 87; c = 0;
Δ = b2-4ac
Δ = 872-4·(-60)·0
Δ = 7569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7569}=87$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(87)-87}{2*-60}=\frac{-174}{-120}
=1+9/20
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(87)+87}{2*-60}=\frac{0}{-120}
=0
$