8/(y+20)=12y

Solution for 8/(y+20)=12y equation:

8/(y+20)=12y

We move all terms to the left:

8/(y+20)-(12y)=0


Domain of the equation: (y+20)!=0

We move all terms containing y to the left, all other terms to the right

y!=-20

y∈R


We add all the numbers together, and all the variables

-12y+8/(y+20)=0

We multiply all the terms by the denominator


-12y*(y+20)+8=0

We multiply parentheses

-12y^2-240y+8=0

a = -12; b = -240; c = +8;
Δ = b2-4ac
Δ = -2402-4·(-12)·8
Δ = 57984
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:

$\sqrt{\Delta}=\sqrt{57984}=\sqrt{64*906}=\sqrt{64}*\sqrt{906}=8\sqrt{906}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-8\sqrt{906}}{2*-12}=\frac{240-8\sqrt{906}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+8\sqrt{906}}{2*-12}=\frac{240+8\sqrt{906}}{-24}
$