F(x)=x^2+4x-21=0

Solution for F(x)=x^2+4x-21=0 equation:

(F)=F^2+4F-21=0

We move all terms to the left:

(F)-(F^2+4F-21)=0

We get rid of parentheses

-F^2+F-4F+21=0

We add all the numbers together, and all the variables

-1F^2-3F+21=0

a = -1; b = -3; c = +21;
Δ = b2-4ac
Δ = -32-4·(-1)·21
Δ = 93
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{-(-3)-\sqrt{93}}{2*-1}=\frac{3-\sqrt{93}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{93}}{2*-1}=\frac{3+\sqrt{93}}{-2}
$