F(x)=20/4x-19

Solution for F(x)=20/4x-19 equation:

(F)=20/4F-19

We move all terms to the left:

(F)-(20/4F-19)=0


Domain of the equation: 4F-19)!=0

F∈R


We get rid of parentheses

F-20/4F+19=0

We multiply all the terms by the denominator


F*4F+19*4F-20=0

Wy multiply elements

4F^2+76F-20=0

a = 4; b = 76; c = -20;
Δ = b2-4ac
Δ = 762-4·4·(-20)
Δ = 6096
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:

$\sqrt{\Delta}=\sqrt{6096}=\sqrt{16*381}=\sqrt{16}*\sqrt{381}=4\sqrt{381}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-4\sqrt{381}}{2*4}=\frac{-76-4\sqrt{381}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+4\sqrt{381}}{2*4}=\frac{-76+4\sqrt{381}}{8}
$