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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1F^2+8F+21=0

a = -1; b = 8; c = +21;
Δ = b2-4ac
Δ = 82-4·(-1)·21
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{37}}{2*-1}=\frac{-8-2\sqrt{37}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{37}}{2*-1}=\frac{-8+2\sqrt{37}}{-2}
$