-w^2=-2w-63

Solution for -w^2=-2w-63 equation:

-w^2=-2w-63

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1w^2-(-2w-63)=0

We get rid of parentheses

-1w^2+2w+63=0

a = -1; b = 2; c = +63;
Δ = b2-4ac
Δ = 22-4·(-1)·63
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-16}{2*-1}=\frac{-18}{-2}
=+9
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+16}{2*-1}=\frac{14}{-2}
=-7
$