F(w)=8w2+28w

Solution for F(w)=8w2+28w equation:

(F)=8F^2+28F

We move all terms to the left:

(F)-(8F^2+28F)=0

We get rid of parentheses

-8F^2+F-28F=0

We add all the numbers together, and all the variables

-8F^2-27F=0

a = -8; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·(-8)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*-8}=\frac{0}{-16}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*-8}=\frac{54}{-16}
=-3+3/8
$