3y-8=1/2y

Solution for 3y-8=1/2y equation:

3y-8=1/2y

We move all terms to the left:

3y-8-(1/2y)=0


Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

3y-(+1/2y)-8=0

We get rid of parentheses

3y-1/2y-8=0

We multiply all the terms by the denominator


3y*2y-8*2y-1=0

Wy multiply elements

6y^2-16y-1=0

a = 6; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·6·(-1)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{70}}{2*6}=\frac{16-2\sqrt{70}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{70}}{2*6}=\frac{16+2\sqrt{70}}{12}
$