32-16/3y+3y=9

Solution for 32-16/3y+3y=9 equation:

32-16/3y+3y=9

We move all terms to the left:

32-16/3y+3y-(9)=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-16/3y+23=0

We multiply all the terms by the denominator


3y*3y+23*3y-16=0

Wy multiply elements

9y^2+69y-16=0

a = 9; b = 69; c = -16;
Δ = b2-4ac
Δ = 692-4·9·(-16)
Δ = 5337
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:

$\sqrt{\Delta}=\sqrt{5337}=\sqrt{9*593}=\sqrt{9}*\sqrt{593}=3\sqrt{593}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-3\sqrt{593}}{2*9}=\frac{-69-3\sqrt{593}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+3\sqrt{593}}{2*9}=\frac{-69+3\sqrt{593}}{18}
$