X^2-24x+144=81

Solution for X^2-24x+144=81 equation:

X^2-24X+144=81

We move all terms to the left:

X^2-24X+144-(81)=0

We add all the numbers together, and all the variables

X^2-24X+63=0

a = 1; b = -24; c = +63;
Δ = b2-4ac
Δ = -242-4·1·63
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-18}{2*1}=\frac{6}{2}
=3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+18}{2*1}=\frac{42}{2}
=21
$