F(x)=2x-8/6x+1

Solution for F(x)=2x-8/6x+1 equation:

(F)=2F-8/6F+1

We move all terms to the left:

(F)-(2F-8/6F+1)=0


Domain of the equation: 6F+1)!=0

F∈R


We get rid of parentheses

F-2F+8/6F-1=0

We multiply all the terms by the denominator


F*6F-2F*6F-1*6F+8=0

Wy multiply elements

6F^2-12F^2-6F+8=0

We add all the numbers together, and all the variables

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

a = -6; b = -6; c = +8;
Δ = b2-4ac
Δ = -62-4·(-6)·8
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{57}}{2*-6}=\frac{6-2\sqrt{57}}{-12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{57}}{2*-6}=\frac{6+2\sqrt{57}}{-12}
$