0=w^2-8w-48

Solution for 0=w^2-8w-48 equation:

0=w^2-8w-48

We move all terms to the left:

0-(w^2-8w-48)=0

We add all the numbers together, and all the variables

-(w^2-8w-48)=0

We get rid of parentheses

-w^2+8w+48=0

We add all the numbers together, and all the variables

-1w^2+8w+48=0

a = -1; b = 8; c = +48;
Δ = b2-4ac
Δ = 82-4·(-1)·48
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{-(8)-16}{2*-1}=\frac{-24}{-2}
=+12
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16}{2*-1}=\frac{8}{-2}
=-4
$