9n+4=3n^2+.75

Solution for 9n+4=3n^2+.75 equation:

9n+4=3n^2+.75

We move all terms to the left:

9n+4-(3n^2+.75)=0

We get rid of parentheses

-3n^2+9n-.75+4=0

We add all the numbers together, and all the variables

-3n^2+9n+3.25=0

a = -3; b = 9; c = +3.25;
Δ = b2-4ac
Δ = 92-4·(-3)·3.25
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-2\sqrt{30}}{2*-3}=\frac{-9-2\sqrt{30}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+2\sqrt{30}}{2*-3}=\frac{-9+2\sqrt{30}}{-6}
$