1/3y+3=8-16y

Solution for 1/3y+3=8-16y equation:

1/3y+3=8-16y

We move all terms to the left:

1/3y+3-(8-16y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

1/3y-(-16y+8)+3=0

We get rid of parentheses

1/3y+16y-8+3=0

We multiply all the terms by the denominator


16y*3y-8*3y+3*3y+1=0

Wy multiply elements

48y^2-24y+9y+1=0

We add all the numbers together, and all the variables

48y^2-15y+1=0

a = 48; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·48·1
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{33}}{2*48}=\frac{15-\sqrt{33}}{96}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{33}}{2*48}=\frac{15+\sqrt{33}}{96}
$