F(-4x)=1/2x-3

Solution for F(-4x)=1/2x-3 equation:

(-4F)=1/2F-3

We move all terms to the left:

(-4F)-(1/2F-3)=0


Domain of the equation: 2F-3)!=0

F∈R


We get rid of parentheses

-4F-1/2F+3=0

We multiply all the terms by the denominator


-4F*2F+3*2F-1=0

Wy multiply elements

-8F^2+6F-1=0

a = -8; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·(-8)·(-1)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2}{2*-8}=\frac{-8}{-16}
=1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2}{2*-8}=\frac{-4}{-16}
=1/4
$