9(3y-2)=y2

Solution for 9(3y-2)=y2 equation:

9(3y-2)=y2

We move all terms to the left:

9(3y-2)-(y2)=0

We add all the numbers together, and all the variables

-1y^2+9(3y-2)=0

We multiply parentheses

-1y^2+27y-18=0

a = -1; b = 27; c = -18;
Δ = b2-4ac
Δ = 272-4·(-1)·(-18)
Δ = 657
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:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{73}}{2*-1}=\frac{-27-3\sqrt{73}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{73}}{2*-1}=\frac{-27+3\sqrt{73}}{-2}
$