1/3y+y=68

Solution for 1/3y+y=68 equation:

1/3y+y=68

We move all terms to the left:

1/3y+y-(68)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

y+1/3y-68=0

We multiply all the terms by the denominator


y*3y-68*3y+1=0

Wy multiply elements

3y^2-204y+1=0

a = 3; b = -204; c = +1;
Δ = b2-4ac
Δ = -2042-4·3·1
Δ = 41604
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:

$\sqrt{\Delta}=\sqrt{41604}=\sqrt{4*10401}=\sqrt{4}*\sqrt{10401}=2\sqrt{10401}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-204)-2\sqrt{10401}}{2*3}=\frac{204-2\sqrt{10401}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-204)+2\sqrt{10401}}{2*3}=\frac{204+2\sqrt{10401}}{6}
$