F(x)=1/7x-49

Solution for F(x)=1/7x-49 equation:

(F)=1/7F-49

We move all terms to the left:

(F)-(1/7F-49)=0


Domain of the equation: 7F-49)!=0

F∈R


We get rid of parentheses

F-1/7F+49=0

We multiply all the terms by the denominator


F*7F+49*7F-1=0

Wy multiply elements

7F^2+343F-1=0

a = 7; b = 343; c = -1;
Δ = b2-4ac
Δ = 3432-4·7·(-1)
Δ = 117677
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{-(343)-\sqrt{117677}}{2*7}=\frac{-343-\sqrt{117677}}{14}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(343)+\sqrt{117677}}{2*7}=\frac{-343+\sqrt{117677}}{14}
$