F(1)=x-7/4x+4

Solution for F(1)=x-7/4x+4 equation:

(1)=F-7/4F+4

We move all terms to the left:

(1)-(F-7/4F+4)=0


Domain of the equation: 4F+4)!=0

F∈R


We get rid of parentheses

-F+7/4F-4+1=0

We multiply all the terms by the denominator


-F*4F-4*4F+1*4F+7=0

Wy multiply elements

-4F^2-16F+4F+7=0

We add all the numbers together, and all the variables

-4F^2-12F+7=0

a = -4; b = -12; c = +7;
Δ = b2-4ac
Δ = -122-4·(-4)·7
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-16}{2*-4}=\frac{-4}{-8}
=1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+16}{2*-4}=\frac{28}{-8}
=-3+1/2
$