2n+5n^2-9=9n

Solution for 2n+5n^2-9=9n equation:

2n+5n^2-9=9n

We move all terms to the left:

2n+5n^2-9-(9n)=0

We add all the numbers together, and all the variables

5n^2-7n-9=0

a = 5; b = -7; c = -9;
Δ = b2-4ac
Δ = -72-4·5·(-9)
Δ = 229
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{229}}{2*5}=\frac{7-\sqrt{229}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{229}}{2*5}=\frac{7+\sqrt{229}}{10}
$