F(x)=3/7x

Solution for F(x)=3/7x equation:

(F)=3/7F

We move all terms to the left:

(F)-(3/7F)=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-(+3/7F)=0

We get rid of parentheses

F-3/7F=0

We multiply all the terms by the denominator


F*7F-3=0

Wy multiply elements

7F^2-3=0

a = 7; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·7·(-3)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{21}}{2*7}=\frac{0-2\sqrt{21}}{14}
=-\frac{2\sqrt{21}}{14}
=-\frac{\sqrt{21}}{7}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{21}}{2*7}=\frac{0+2\sqrt{21}}{14}
=\frac{2\sqrt{21}}{14}
=\frac{\sqrt{21}}{7}
$