(x^2-18x-63=0)

Solution for (x^2-18x-63=0) equation:

(x^2-18x-63=0)

We move all terms to the left:

(x^2-18x-63-(0))=0

We get rid of parentheses

x^2-18x-63-0=0

We add all the numbers together, and all the variables

x^2-18x-63=0

a = 1; b = -18; c = -63;
Δ = b2-4ac
Δ = -182-4·1·(-63)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-24}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+24}{2*1}=\frac{42}{2}
=21
$