3/4y+4=11/12y-9

Solution for 3/4y+4=11/12y-9 equation:

3/4y+4=11/12y-9

We move all terms to the left:

3/4y+4-(11/12y-9)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 12y-9)!=0

y∈R


We get rid of parentheses

3/4y-11/12y+9+4=0

We calculate fractions


36y/48y^2+(-44y)/48y^2+9+4=0

We add all the numbers together, and all the variables

36y/48y^2+(-44y)/48y^2+13=0

We multiply all the terms by the denominator


36y+(-44y)+13*48y^2=0

Wy multiply elements

624y^2+36y+(-44y)=0

We get rid of parentheses

624y^2+36y-44y=0

We add all the numbers together, and all the variables

624y^2-8y=0

a = 624; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·624·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*624}=\frac{0}{1248}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*624}=\frac{16}{1248}
=1/78
$