F(x)=4-1/5x

Solution for F(x)=4-1/5x equation:

(F)=4-1/5F

We move all terms to the left:

(F)-(4-1/5F)=0


Domain of the equation: 5F)!=0

F!=0/1

F!=0

F∈R


We add all the numbers together, and all the variables

F-(-1/5F+4)=0

We get rid of parentheses

F+1/5F-4=0

We multiply all the terms by the denominator


F*5F-4*5F+1=0

Wy multiply elements

5F^2-20F+1=0

a = 5; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·5·1
Δ = 380
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:

$\sqrt{\Delta}=\sqrt{380}=\sqrt{4*95}=\sqrt{4}*\sqrt{95}=2\sqrt{95}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{95}}{2*5}=\frac{20-2\sqrt{95}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{95}}{2*5}=\frac{20+2\sqrt{95}}{10}
$