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

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

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

We move all terms to the left:

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


Domain of the equation: yy!=0

y!=0/1

y!=0

y∈R



Domain of the equation: 4y+10)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


12y/4y^2+(-y)/4y^2-10-6=0

We add all the numbers together, and all the variables

12y/4y^2+(-1y)/4y^2-10-6=0

We add all the numbers together, and all the variables

12y/4y^2+(-1y)/4y^2-16=0

We multiply all the terms by the denominator


12y+(-1y)-16*4y^2=0

Wy multiply elements

-64y^2+12y+(-1y)=0

We get rid of parentheses

-64y^2+12y-1y=0

We add all the numbers together, and all the variables

-64y^2+11y=0

a = -64; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-64)·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*-64}=\frac{-22}{-128}
=11/64
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-64}=\frac{0}{-128}
=0
$