w=w^2+2w-8

Solution for w=w^2+2w-8 equation:

w=w^2+2w-8

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -1; b = -1; c = +8;
Δ = b2-4ac
Δ = -12-4·(-1)·8
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{33}}{2*-1}=\frac{1-\sqrt{33}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{33}}{2*-1}=\frac{1+\sqrt{33}}{-2}
$