F(x)=1/7x-21

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

(F)=1/7F-21

We move all terms to the left:

(F)-(1/7F-21)=0


Domain of the equation: 7F-21)!=0

F∈R


We get rid of parentheses

F-1/7F+21=0

We multiply all the terms by the denominator


F*7F+21*7F-1=0

Wy multiply elements

7F^2+147F-1=0

a = 7; b = 147; c = -1;
Δ = b2-4ac
Δ = 1472-4·7·(-1)
Δ = 21637
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(147)-\sqrt{21637}}{2*7}=\frac{-147-\sqrt{21637}}{14}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(147)+\sqrt{21637}}{2*7}=\frac{-147+\sqrt{21637}}{14}
$