(y-11)3y=1

Solution for (y-11)3y=1 equation:

(y-11)3y=1

We move all terms to the left:

(y-11)3y-(1)=0

We multiply parentheses

3y^2-33y-1=0

a = 3; b = -33; c = -1;
Δ = b2-4ac
Δ = -332-4·3·(-1)
Δ = 1101
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{-(-33)-\sqrt{1101}}{2*3}=\frac{33-\sqrt{1101}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{1101}}{2*3}=\frac{33+\sqrt{1101}}{6}
$