F(x)=2x-6/4x+8

Solution for F(x)=2x-6/4x+8 equation:

(F)=2F-6/4F+8

We move all terms to the left:

(F)-(2F-6/4F+8)=0


Domain of the equation: 4F+8)!=0

F∈R


We get rid of parentheses

F-2F+6/4F-8=0

We multiply all the terms by the denominator


F*4F-2F*4F-8*4F+6=0

Wy multiply elements

4F^2-8F^2-32F+6=0

We add all the numbers together, and all the variables

-4F^2-32F+6=0

a = -4; b = -32; c = +6;
Δ = b2-4ac
Δ = -322-4·(-4)·6
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{70}}{2*-4}=\frac{32-4\sqrt{70}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{70}}{2*-4}=\frac{32+4\sqrt{70}}{-8}
$