y^2=27-6y

Solution for y^2=27-6y equation:

y^2=27-6y

We move all terms to the left:

y^2-(27-6y)=0

We add all the numbers together, and all the variables

y^2-(-6y+27)=0

We get rid of parentheses

y^2+6y-27=0

a = 1; b = 6; c = -27;
Δ = b2-4ac
Δ = 62-4·1·(-27)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12}{2*1}=\frac{-18}{2}
=-9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12}{2*1}=\frac{6}{2}
=3
$