2y(y-4)=9-y

Solution for 2y(y-4)=9-y equation:

2y(y-4)=9-y

We move all terms to the left:

2y(y-4)-(9-y)=0

We add all the numbers together, and all the variables

2y(y-4)-(-1y+9)=0

We multiply parentheses

2y^2-8y-(-1y+9)=0

We get rid of parentheses

2y^2-8y+1y-9=0

We add all the numbers together, and all the variables

2y^2-7y-9=0

a = 2; b = -7; c = -9;
Δ = b2-4ac
Δ = -72-4·2·(-9)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-11}{2*2}=\frac{-4}{4}
=-1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+11}{2*2}=\frac{18}{4}
=4+1/2
$