12y-2y2-54+9y=0

Solution for 12y-2y2-54+9y=0 equation:

12y-2y^2-54+9y=0

We add all the numbers together, and all the variables

-2y^2+21y-54=0

a = -2; b = 21; c = -54;
Δ = b2-4ac
Δ = 212-4·(-2)·(-54)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3}{2*-2}=\frac{-24}{-4}
=+6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3}{2*-2}=\frac{-18}{-4}
=4+1/2
$