F(x)=x^2/4-5

Solution for F(x)=x^2/4-5 equation:

(F)=F^2/4-5

We move all terms to the left:

(F)-(F^2/4-5)=0

We get rid of parentheses

-F^2/4+F+5=0

We multiply all the terms by the denominator


-F^2+F*4+5*4=0

We add all the numbers together, and all the variables

-1F^2+F*4+20=0

Wy multiply elements

-1F^2+4F+20=0

a = -1; b = 4; c = +20;
Δ = b2-4ac
Δ = 42-4·(-1)·20
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{6}}{2*-1}=\frac{-4-4\sqrt{6}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{6}}{2*-1}=\frac{-4+4\sqrt{6}}{-2}
$