12/y=4+3y

Solution for 12/y=4+3y equation:

12/y=4+3y

We move all terms to the left:

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


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

12/y-3y-4=0

We multiply all the terms by the denominator


-3y*y-4*y+12=0

We add all the numbers together, and all the variables

-4y-3y*y+12=0

Wy multiply elements

-3y^2-4y+12=0

a = -3; b = -4; c = +12;
Δ = b2-4ac
Δ = -42-4·(-3)·12
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{10}}{2*-3}=\frac{4-4\sqrt{10}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{10}}{2*-3}=\frac{4+4\sqrt{10}}{-6}
$