x2-81=24x

Solution for x2-81=24x equation:

x2-81=24x

We move all terms to the left:

x2-81-(24x)=0

We add all the numbers together, and all the variables

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