F(x)=7x^2+21x+8

Solution for F(x)=7x^2+21x+8 equation:

(F)=7F^2+21F+8

We move all terms to the left:

(F)-(7F^2+21F+8)=0

We get rid of parentheses

-7F^2+F-21F-8=0

We add all the numbers together, and all the variables

-7F^2-20F-8=0

a = -7; b = -20; c = -8;
Δ = b2-4ac
Δ = -202-4·(-7)·(-8)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{11}}{2*-7}=\frac{20-4\sqrt{11}}{-14}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{11}}{2*-7}=\frac{20+4\sqrt{11}}{-14}
$