y(4y-5)=9

Solution for y(4y-5)=9 equation:

y(4y-5)=9

We move all terms to the left:

y(4y-5)-(9)=0

We multiply parentheses

4y^2-5y-9=0

a = 4; b = -5; c = -9;
Δ = b2-4ac
Δ = -52-4·4·(-9)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-13}{2*4}=\frac{-8}{8}
=-1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+13}{2*4}=\frac{18}{8}
=2+1/4
$