-3/4y=9+y

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

-3/4y=9+y

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-3/4y-y-9=0

We multiply all the terms by the denominator


-y*4y-9*4y-3=0

Wy multiply elements

-4y^2-36y-3=0

a = -4; b = -36; c = -3;
Δ = b2-4ac
Δ = -362-4·(-4)·(-3)
Δ = 1248
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{78}}{2*-4}=\frac{36-4\sqrt{78}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{78}}{2*-4}=\frac{36+4\sqrt{78}}{-8}
$