F(x)=7x^2-21x-14

Solution for F(x)=7x^2-21x-14 equation:

(F)=7F^2-21F-14

We move all terms to the left:

(F)-(7F^2-21F-14)=0

We get rid of parentheses

-7F^2+F+21F+14=0

We add all the numbers together, and all the variables

-7F^2+22F+14=0

a = -7; b = 22; c = +14;
Δ = b2-4ac
Δ = 222-4·(-7)·14
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{219}}{2*-7}=\frac{-22-2\sqrt{219}}{-14}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{219}}{2*-7}=\frac{-22+2\sqrt{219}}{-14}
$