3/4y-6=1/y+10

Solution for 3/4y-6=1/y+10 equation:

3/4y-6=1/y+10

We move all terms to the left:

3/4y-6-(1/y+10)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: y+10)!=0

y∈R


We get rid of parentheses

3/4y-1/y-10-6=0

We calculate fractions


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

We add all the numbers together, and all the variables

3y/4y^2+(-4y)/4y^2-16=0

We multiply all the terms by the denominator


3y+(-4y)-16*4y^2=0

Wy multiply elements

-64y^2+3y+(-4y)=0

We get rid of parentheses

-64y^2+3y-4y=0

We add all the numbers together, and all the variables

-64y^2-1y=0

a = -64; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-64)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-64}=\frac{0}{-128}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-64}=\frac{2}{-128}
=-1/64
$