(28-y)/y=3y+4

Solution for (28-y)/y=3y+4 equation:

(28-y)/y=3y+4

We move all terms to the left:

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


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

(-1y+28)/y-(3y+4)=0

We get rid of parentheses

(-1y+28)/y-3y-4=0

We multiply all the terms by the denominator


(-1y+28)-3y*y-4*y=0

We add all the numbers together, and all the variables

-4y+(-1y+28)-3y*y=0

Wy multiply elements

-3y^2-4y+(-1y+28)=0

We get rid of parentheses

-3y^2-4y-1y+28=0

We add all the numbers together, and all the variables

-3y^2-5y+28=0

a = -3; b = -5; c = +28;
Δ = b2-4ac
Δ = -52-4·(-3)·28
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-19}{2*-3}=\frac{-14}{-6}
=2+1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+19}{2*-3}=\frac{24}{-6}
=-4
$