1/3y+5y=32

Solution for 1/3y+5y=32 equation:

1/3y+5y=32

We move all terms to the left:

1/3y+5y-(32)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

5y+1/3y-32=0

We multiply all the terms by the denominator


5y*3y-32*3y+1=0

Wy multiply elements

15y^2-96y+1=0

a = 15; b = -96; c = +1;
Δ = b2-4ac
Δ = -962-4·15·1
Δ = 9156
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:

$\sqrt{\Delta}=\sqrt{9156}=\sqrt{4*2289}=\sqrt{4}*\sqrt{2289}=2\sqrt{2289}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-2\sqrt{2289}}{2*15}=\frac{96-2\sqrt{2289}}{30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+2\sqrt{2289}}{2*15}=\frac{96+2\sqrt{2289}}{30}
$