9n+1=3n^2-0.75

Solution for 9n+1=3n^2-0.75 equation:

9n+1=3n^2-0.75

We move all terms to the left:

9n+1-(3n^2-0.75)=0

We get rid of parentheses

-3n^2+9n+0.75+1=0

We add all the numbers together, and all the variables

-3n^2+9n+1.75=0

a = -3; b = 9; c = +1.75;
Δ = b2-4ac
Δ = 92-4·(-3)·1.75
Δ = 102
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{-(9)-\sqrt{102}}{2*-3}=\frac{-9-\sqrt{102}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{102}}{2*-3}=\frac{-9+\sqrt{102}}{-6}
$