0=w^2+18w-63

Solution for 0=w^2+18w-63 equation:

0=w^2+18w-63

We move all terms to the left:

0-(w^2+18w-63)=0

We add all the numbers together, and all the variables

-(w^2+18w-63)=0

We get rid of parentheses

-w^2-18w+63=0

We add all the numbers together, and all the variables

-1w^2-18w+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:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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