11=9y(5y+1)

Solution for 11=9y(5y+1) equation:

11=9y(5y+1)

We move all terms to the left:

11-(9y(5y+1))=0


We calculate terms in parentheses: -(9y(5y+1)), so:

9y(5y+1)

We multiply parentheses

45y^2+9y

Back to the equation:

-(45y^2+9y)


We get rid of parentheses

-45y^2-9y+11=0

a = -45; b = -9; c = +11;
Δ = b2-4ac
Δ = -92-4·(-45)·11
Δ = 2061
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:

$\sqrt{\Delta}=\sqrt{2061}=\sqrt{9*229}=\sqrt{9}*\sqrt{229}=3\sqrt{229}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{229}}{2*-45}=\frac{9-3\sqrt{229}}{-90}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{229}}{2*-45}=\frac{9+3\sqrt{229}}{-90}
$