F(x)=-x^2/4x-21

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

(F)=-F^2/4F-21

We move all terms to the left:

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


Domain of the equation: 4F-21)!=0

F∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

F^2+4F^2+84F=0

We add all the numbers together, and all the variables

5F^2+84F=0

a = 5; b = 84; c = 0;
Δ = b2-4ac
Δ = 842-4·5·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-84}{2*5}=\frac{-168}{10}
=-16+4/5
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+84}{2*5}=\frac{0}{10}
=0
$