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

Solution for 2y-3y-2y(y-6)=9 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1y-2y(y-6)-9=0

We multiply parentheses

-2y^2-1y+12y-9=0

We add all the numbers together, and all the variables

-2y^2+11y-9=0

a = -2; b = 11; c = -9;
Δ = b2-4ac
Δ = 112-4·(-2)·(-9)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-7}{2*-2}=\frac{-18}{-4}
=4+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+7}{2*-2}=\frac{-4}{-4}
=1
$