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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

4f^2+18f-1=0

a = 4; b = 18; c = -1;
Δ = b2-4ac
Δ = 182-4·4·(-1)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{85}}{2*4}=\frac{-18-2\sqrt{85}}{8}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{85}}{2*4}=\frac{-18+2\sqrt{85}}{8}
$