3/2y-10+4=6/y-5

Solution for 3/2y-10+4=6/y-5 equation:

3/2y-10+4=6/y-5

We move all terms to the left:

3/2y-10+4-(6/y-5)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: y-5)!=0

y∈R


We add all the numbers together, and all the variables

3/2y-(6/y-5)-6=0

We get rid of parentheses

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

We calculate fractions


3y/2y^2+(-12y)/2y^2+5-6=0

We add all the numbers together, and all the variables

3y/2y^2+(-12y)/2y^2-1=0

We multiply all the terms by the denominator


3y+(-12y)-1*2y^2=0

Wy multiply elements

-2y^2+3y+(-12y)=0

We get rid of parentheses

-2y^2+3y-12y=0

We add all the numbers together, and all the variables

-2y^2-9y=0

a = -2; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-2)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-2}=\frac{0}{-4}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-2}=\frac{18}{-4}
=-4+1/2
$