3y^2-6y=9

Solution for 3y^2-6y=9 equation:

3y^2-6y=9

We move all terms to the left:

3y^2-6y-(9)=0

a = 3; b = -6; c = -9;
Δ = b2-4ac
Δ = -62-4·3·(-9)
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*3}=\frac{-6}{6}
=-1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12}{2*3}=\frac{18}{6}
=3
$