5-x^2-9x=0

Solution for 5-x^2-9x=0 equation:

5-x^2-9x=0

We add all the numbers together, and all the variables

-1x^2-9x+5=0

a = -1; b = -9; c = +5;
Δ = b2-4ac
Δ = -92-4·(-1)·5
Δ = 101
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{101}}{2*-1}=\frac{9-\sqrt{101}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{101}}{2*-1}=\frac{9+\sqrt{101}}{-2}
$