F(x)=8x^2+48x+6

Solution for F(x)=8x^2+48x+6 equation:

(F)=8F^2+48F+6

We move all terms to the left:

(F)-(8F^2+48F+6)=0

We get rid of parentheses

-8F^2+F-48F-6=0

We add all the numbers together, and all the variables

-8F^2-47F-6=0

a = -8; b = -47; c = -6;
Δ = b2-4ac
Δ = -472-4·(-8)·(-6)
Δ = 2017
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-\sqrt{2017}}{2*-8}=\frac{47-\sqrt{2017}}{-16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{2017}}{2*-8}=\frac{47+\sqrt{2017}}{-16}
$