Y/6y=8+2y

Solution for Y/6y=8+2y equation:

/6Y=8+2Y

We move all terms to the left:

/6Y-(8+2Y)=0


Domain of the equation: 6Y!=0

Y!=0/6

Y!=0

Y∈R


We add all the numbers together, and all the variables

/6Y-(2Y+8)=0

We get rid of parentheses

/6Y-2Y-8=0

We multiply all the terms by the denominator


-2Y*6Y-8*6Y+=0

We add all the numbers together, and all the variables

-2Y*6Y-8*6Y=0

Wy multiply elements

-12Y^2-48Y=0

a = -12; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·(-12)·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48}{2*-12}=\frac{0}{-24}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*-12}=\frac{96}{-24}
=-4
$