F(x)=1500+500x/x

Solution for F(x)=1500+500x/x equation:

(F)=1500+500F/F

We move all terms to the left:

(F)-(1500+500F/F)=0


Domain of the equation: F)!=0

F!=0/1

F!=0

F∈R


We add all the numbers together, and all the variables

F-(500F/F+1500)=0

We get rid of parentheses

F-500F/F-1500=0

We multiply all the terms by the denominator


F*F-500F-1500*F=0

We add all the numbers together, and all the variables

-2000F+F*F=0

Wy multiply elements

F^2-2000F=0

a = 1; b = -2000; c = 0;
Δ = b2-4ac
Δ = -20002-4·1·0
Δ = 4000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4000000}=2000$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2000)-2000}{2*1}=\frac{0}{2}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2000)+2000}{2*1}=\frac{4000}{2}
=2000
$