F(x)=8x^2+16-42

Solution for F(x)=8x^2+16-42 equation:

(F)=8F^2+16-42

We move all terms to the left:

(F)-(8F^2+16-42)=0

We get rid of parentheses

-8F^2+F-16+42=0

We add all the numbers together, and all the variables

-8F^2+F+26=0

a = -8; b = 1; c = +26;
Δ = b2-4ac
Δ = 12-4·(-8)·26
Δ = 833
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{833}=\sqrt{49*17}=\sqrt{49}*\sqrt{17}=7\sqrt{17}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7\sqrt{17}}{2*-8}=\frac{-1-7\sqrt{17}}{-16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7\sqrt{17}}{2*-8}=\frac{-1+7\sqrt{17}}{-16}
$