F(11)=x-11/5x-3

Solution for F(11)=x-11/5x-3 equation:

(11)=F-11/5F-3

We move all terms to the left:

(11)-(F-11/5F-3)=0


Domain of the equation: 5F-3)!=0

F∈R


We get rid of parentheses

-F+11/5F+3+11=0

We multiply all the terms by the denominator


-F*5F+3*5F+11*5F+11=0

Wy multiply elements

-5F^2+15F+55F+11=0

We add all the numbers together, and all the variables

-5F^2+70F+11=0

a = -5; b = 70; c = +11;
Δ = b2-4ac
Δ = 702-4·(-5)·11
Δ = 5120
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:

$\sqrt{\Delta}=\sqrt{5120}=\sqrt{1024*5}=\sqrt{1024}*\sqrt{5}=32\sqrt{5}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-32\sqrt{5}}{2*-5}=\frac{-70-32\sqrt{5}}{-10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+32\sqrt{5}}{2*-5}=\frac{-70+32\sqrt{5}}{-10}
$