F(x)=5x-2/2x+1

Solution for F(x)=5x-2/2x+1 equation:

(F)=5F-2/2F+1

We move all terms to the left:

(F)-(5F-2/2F+1)=0


Domain of the equation: 2F+1)!=0

F∈R


We get rid of parentheses

F-5F+2/2F-1=0

We multiply all the terms by the denominator


F*2F-5F*2F-1*2F+2=0

Wy multiply elements

2F^2-10F^2-2F+2=0

We add all the numbers together, and all the variables

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

a = -8; b = -2; c = +2;
Δ = b2-4ac
Δ = -22-4·(-8)·2
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{17}}{2*-8}=\frac{2-2\sqrt{17}}{-16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{17}}{2*-8}=\frac{2+2\sqrt{17}}{-16}
$