F(4-2x)=1/2x-1

Solution for F(4-2x)=1/2x-1 equation:

(4-2F)=1/2F-1

We move all terms to the left:

(4-2F)-(1/2F-1)=0


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

F∈R


We add all the numbers together, and all the variables

(-2F+4)-(1/2F-1)=0

We get rid of parentheses

-2F-1/2F+4+1=0

We multiply all the terms by the denominator


-2F*2F+4*2F+1*2F-1=0

Wy multiply elements

-4F^2+8F+2F-1=0

We add all the numbers together, and all the variables

-4F^2+10F-1=0

a = -4; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·(-4)·(-1)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{21}}{2*-4}=\frac{-10-2\sqrt{21}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{21}}{2*-4}=\frac{-10+2\sqrt{21}}{-8}
$