24x+81=x^2

Solution for 24x+81=x^2 equation:

24x+81=x^2

We move all terms to the left:

24x+81-(x^2)=0

determiningTheFunctionDomain
-x^2+24x+81=0

We add all the numbers together, and all the variables

-1x^2+24x+81=0

a = -1; b = 24; c = +81;
Δ = b2-4ac
Δ = 242-4·(-1)·81
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-30}{2*-1}=\frac{-54}{-2}
=+27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+30}{2*-1}=\frac{6}{-2}
=-3
$