-3n-3n(-3n+9)+1=58

Solution for -3n-3n(-3n+9)+1=58 equation:

-3n-3n(-3n+9)+1=58

We move all terms to the left:

-3n-3n(-3n+9)+1-(58)=0

We add all the numbers together, and all the variables

-3n-3n(-3n+9)-57=0

We multiply parentheses

9n^2-3n-27n-57=0

We add all the numbers together, and all the variables

9n^2-30n-57=0

a = 9; b = -30; c = -57;
Δ = b2-4ac
Δ = -302-4·9·(-57)
Δ = 2952
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2952}=\sqrt{36*82}=\sqrt{36}*\sqrt{82}=6\sqrt{82}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{82}}{2*9}=\frac{30-6\sqrt{82}}{18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{82}}{2*9}=\frac{30+6\sqrt{82}}{18}
$