F(x)=1/7x-9,x=21

Solution for F(x)=1/7x-9,x=21 equation:

(F)=1/7F-9.F=21

We move all terms to the left:

(F)-(1/7F-9.F)=0


Domain of the equation: 7F-9.F)!=0

F∈R


We add all the numbers together, and all the variables

F-(-9F+1/7F)=0

We get rid of parentheses

F+9F-1/7F=0

We multiply all the terms by the denominator


F*7F+9F*7F-1=0

Wy multiply elements

7F^2+63F^2-1=0

We add all the numbers together, and all the variables

70F^2-1=0

a = 70; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·70·(-1)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{70}}{2*70}=\frac{0-2\sqrt{70}}{140}
=-\frac{2\sqrt{70}}{140}
=-\frac{\sqrt{70}}{70}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{70}}{2*70}=\frac{0+2\sqrt{70}}{140}
=\frac{2\sqrt{70}}{140}
=\frac{\sqrt{70}}{70}
$