F(-x)=2x+3/7x-9

Solution for F(-x)=2x+3/7x-9 equation:

(-F)=2F+3/7F-9

We move all terms to the left:

(-F)-(2F+3/7F-9)=0


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

F∈R


We add all the numbers together, and all the variables

(-1F)-(2F+3/7F-9)=0

We get rid of parentheses

-1F-2F-3/7F+9=0

We multiply all the terms by the denominator


-1F*7F-2F*7F+9*7F-3=0

Wy multiply elements

-7F^2-14F^2+63F-3=0

We add all the numbers together, and all the variables

-21F^2+63F-3=0

a = -21; b = 63; c = -3;
Δ = b2-4ac
Δ = 632-4·(-21)·(-3)
Δ = 3717
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:

$\sqrt{\Delta}=\sqrt{3717}=\sqrt{9*413}=\sqrt{9}*\sqrt{413}=3\sqrt{413}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-3\sqrt{413}}{2*-21}=\frac{-63-3\sqrt{413}}{-42}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+3\sqrt{413}}{2*-21}=\frac{-63+3\sqrt{413}}{-42}
$