3y-5y(y-9)=-1

Solution for 3y-5y(y-9)=-1 equation:

3y-5y(y-9)=-1

We move all terms to the left:

3y-5y(y-9)-(-1)=0

We add all the numbers together, and all the variables

3y-5y(y-9)+1=0

We multiply parentheses

-5y^2+3y+45y+1=0

We add all the numbers together, and all the variables

-5y^2+48y+1=0

a = -5; b = 48; c = +1;
Δ = b2-4ac
Δ = 482-4·(-5)·1
Δ = 2324
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:

$\sqrt{\Delta}=\sqrt{2324}=\sqrt{4*581}=\sqrt{4}*\sqrt{581}=2\sqrt{581}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-2\sqrt{581}}{2*-5}=\frac{-48-2\sqrt{581}}{-10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+2\sqrt{581}}{2*-5}=\frac{-48+2\sqrt{581}}{-10}
$