2y^2-9y=-9

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

2y^2-9y=-9

We move all terms to the left:

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

We add all the numbers together, and all the variables

2y^2-9y+9=0

a = 2; b = -9; c = +9;
Δ = b2-4ac
Δ = -92-4·2·9
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{-(-9)-3}{2*2}=\frac{6}{4}
=1+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3}{2*2}=\frac{12}{4}
=3
$