9x-x^2-4=0

Solution for 9x-x^2-4=0 equation:

9x-x^2-4=0

We add all the numbers together, and all the variables

-1x^2+9x-4=0

a = -1; b = 9; c = -4;
Δ = b2-4ac
Δ = 92-4·(-1)·(-4)
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{65}}{2*-1}=\frac{-9-\sqrt{65}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{65}}{2*-1}=\frac{-9+\sqrt{65}}{-2}
$