3^2-3(y)+y^2=27

Solution for 3^2-3(y)+y^2=27 equation:

3^2-3(y)+y^2=27

We move all terms to the left:

3^2-3(y)+y^2-(27)=0

determiningTheFunctionDomain
y^2-3y-27+3^2=0

We add all the numbers together, and all the variables

y^2-3y-18=0

a = 1; b = -3; c = -18;
Δ = b2-4ac
Δ = -32-4·1·(-18)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-9}{2*1}=\frac{-6}{2}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+9}{2*1}=\frac{12}{2}
=6
$