11f-(-2+f);f=1/2

Solution for 11f-(-2+f);f=1/2 equation:

11f-(-2+f)f=1/2

We move all terms to the left:

11f-(-2+f)f-(1/2)=0

We add all the numbers together, and all the variables

11f-(f-2)f-(+1/2)=0

We multiply parentheses

-f^2+11f+2f-(+1/2)=0

We get rid of parentheses

-f^2+11f+2f-1/2=0

We multiply all the terms by the denominator


-f^2*2+11f*2+2f*2-1=0

Wy multiply elements

-2f^2+22f+4f-1=0

We add all the numbers together, and all the variables

-2f^2+26f-1=0

a = -2; b = 26; c = -1;
Δ = b2-4ac
Δ = 262-4·(-2)·(-1)
Δ = 668
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:

$\sqrt{\Delta}=\sqrt{668}=\sqrt{4*167}=\sqrt{4}*\sqrt{167}=2\sqrt{167}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{167}}{2*-2}=\frac{-26-2\sqrt{167}}{-4}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{167}}{2*-2}=\frac{-26+2\sqrt{167}}{-4}
$