0=2n^2+5n-9

Solution for 0=2n^2+5n-9 equation:

0=2n^2+5n-9

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

a = -2; b = -5; c = +9;
Δ = b2-4ac
Δ = -52-4·(-2)·9
Δ = 97
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{-(-5)-\sqrt{97}}{2*-2}=\frac{5-\sqrt{97}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{97}}{2*-2}=\frac{5+\sqrt{97}}{-4}
$