1/3y+3y=8

Solution for 1/3y+3y=8 equation:

1/3y+3y=8

We move all terms to the left:

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


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

3y+1/3y-8=0

We multiply all the terms by the denominator


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

Wy multiply elements

9y^2-24y+1=0

a = 9; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·9·1
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{15}}{2*9}=\frac{24-6\sqrt{15}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{15}}{2*9}=\frac{24+6\sqrt{15}}{18}
$