F(x)=5x/x*2-3x

Solution for F(x)=5x/x*2-3x equation:

(F)=5F/F*2-3F

We move all terms to the left:

(F)-(5F/F*2-3F)=0


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

F∈R


We add all the numbers together, and all the variables

F-(-3F+5F/F*2)=0

We get rid of parentheses

F+3F-5F/F*2=0

We multiply all the terms by the denominator


F*F*2+3F*F*2-5F=0

We add all the numbers together, and all the variables

-5F+F*F*2+3F*F*2=0

Wy multiply elements

2F^2*2+6F^2*2-5F=0

Wy multiply elements

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

We add all the numbers together, and all the variables

16F^2-5F=0

a = 16; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·16·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*16}=\frac{0}{32}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*16}=\frac{10}{32}
=5/16
$