-11f=7f(1-2f)+5

Solution for -11f=7f(1-2f)+5 equation:

-11f=7f(1-2f)+5

We move all terms to the left:

-11f-(7f(1-2f)+5)=0

We add all the numbers together, and all the variables

-11f-(7f(-2f+1)+5)=0


We calculate terms in parentheses: -(7f(-2f+1)+5), so:

7f(-2f+1)+5

We multiply parentheses

-14f^2+7f+5

Back to the equation:

-(-14f^2+7f+5)


We get rid of parentheses

14f^2-7f-11f-5=0

We add all the numbers together, and all the variables

14f^2-18f-5=0

a = 14; b = -18; c = -5;
Δ = b2-4ac
Δ = -182-4·14·(-5)
Δ = 604
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:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{151}}{2*14}=\frac{18-2\sqrt{151}}{28}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{151}}{2*14}=\frac{18+2\sqrt{151}}{28}
$