F(x)=5x/4x+3

Solution for F(x)=5x/4x+3 equation:

(F)=5F/4F+3

We move all terms to the left:

(F)-(5F/4F+3)=0


Domain of the equation: 4F+3)!=0

F∈R


We get rid of parentheses

F-5F/4F-3=0

We multiply all the terms by the denominator


F*4F-5F-3*4F=0

We add all the numbers together, and all the variables

-5F+F*4F-3*4F=0

Wy multiply elements

4F^2-5F-12F=0

We add all the numbers together, and all the variables

4F^2-17F=0

a = 4; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·4·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*4}=\frac{0}{8}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*4}=\frac{34}{8}
=4+1/4
$