y=2-3y/y-4

Solution for y=2-3y/y-4 equation:

y=2-3y/y-4

We move all terms to the left:

y-(2-3y/y-4)=0


Domain of the equation: y-4)!=0

y∈R


We add all the numbers together, and all the variables

y-(-3y/y-2)=0

We get rid of parentheses

y+3y/y+2=0

We multiply all the terms by the denominator


y*y+3y+2*y=0

We add all the numbers together, and all the variables

5y+y*y=0

Wy multiply elements

y^2+5y=0

a = 1; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·1·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*1}=\frac{-10}{2}
=-5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*1}=\frac{0}{2}
=0
$