w=w^2-318.75

Solution for w=w^2-318.75 equation:

w=w^2-318.75

We move all terms to the left:

w-(w^2-318.75)=0

We get rid of parentheses

-w^2+w+318.75=0

We add all the numbers together, and all the variables

-1w^2+w+318.75=0

a = -1; b = 1; c = +318.75;
Δ = b2-4ac
Δ = 12-4·(-1)·318.75
Δ = 1276
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1276}=\sqrt{4*319}=\sqrt{4}*\sqrt{319}=2\sqrt{319}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-2\sqrt{319}}{2*-1}=\frac{-1-2\sqrt{319}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+2\sqrt{319}}{2*-1}=\frac{-1+2\sqrt{319}}{-2}
$