9/2y+1=10/y+6

Solution for 9/2y+1=10/y+6 equation:

9/2y+1=10/y+6

We move all terms to the left:

9/2y+1-(10/y+6)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: y+6)!=0

y∈R


We get rid of parentheses

9/2y-10/y-6+1=0

We calculate fractions


9y/2y^2+(-20y)/2y^2-6+1=0

We add all the numbers together, and all the variables

9y/2y^2+(-20y)/2y^2-5=0

We multiply all the terms by the denominator


9y+(-20y)-5*2y^2=0

Wy multiply elements

-10y^2+9y+(-20y)=0

We get rid of parentheses

-10y^2+9y-20y=0

We add all the numbers together, and all the variables

-10y^2-11y=0

a = -10; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-10)·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*-10}=\frac{0}{-20}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-10}=\frac{22}{-20}
=-1+1/10
$