9x+18x-x^2=72

Solution for 9x+18x-x^2=72 equation:

9x+18x-x^2=72

We move all terms to the left:

9x+18x-x^2-(72)=0

We add all the numbers together, and all the variables

-1x^2+27x-72=0

a = -1; b = 27; c = -72;
Δ = b2-4ac
Δ = 272-4·(-1)·(-72)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-21}{2*-1}=\frac{-48}{-2}
=+24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+21}{2*-1}=\frac{-6}{-2}
=+3
$