F(x)=5/7x

Solution for F(x)=5/7x equation:

(F)=5/7F

We move all terms to the left:

(F)-(5/7F)=0


Domain of the equation: 7F)!=0

F!=0/1

F!=0

F∈R


We add all the numbers together, and all the variables

F-(+5/7F)=0

We get rid of parentheses

F-5/7F=0

We multiply all the terms by the denominator


F*7F-5=0

Wy multiply elements

7F^2-5=0

a = 7; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·7·(-5)
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{35}}{2*7}=\frac{0-2\sqrt{35}}{14}
=-\frac{2\sqrt{35}}{14}
=-\frac{\sqrt{35}}{7}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{35}}{2*7}=\frac{0+2\sqrt{35}}{14}
=\frac{2\sqrt{35}}{14}
=\frac{\sqrt{35}}{7}
$