9y(y+1)-18y=45

Solution for 9y(y+1)-18y=45 equation:

9y(y+1)-18y=45

We move all terms to the left:

9y(y+1)-18y-(45)=0

We add all the numbers together, and all the variables

-18y+9y(y+1)-45=0

We multiply parentheses

9y^2-18y+9y-45=0

We add all the numbers together, and all the variables

9y^2-9y-45=0

a = 9; b = -9; c = -45;
Δ = b2-4ac
Δ = -92-4·9·(-45)
Δ = 1701
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1701}=\sqrt{81*21}=\sqrt{81}*\sqrt{21}=9\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9\sqrt{21}}{2*9}=\frac{9-9\sqrt{21}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9\sqrt{21}}{2*9}=\frac{9+9\sqrt{21}}{18}
$