F(x)=500-5/8x

Solution for F(x)=500-5/8x equation:

(F)=500-5/8F

We move all terms to the left:

(F)-(500-5/8F)=0


Domain of the equation: 8F)!=0

F!=0/1

F!=0

F∈R


We add all the numbers together, and all the variables

F-(-5/8F+500)=0

We get rid of parentheses

F+5/8F-500=0

We multiply all the terms by the denominator


F*8F-500*8F+5=0

Wy multiply elements

8F^2-4000F+5=0

a = 8; b = -4000; c = +5;
Δ = b2-4ac
Δ = -40002-4·8·5
Δ = 15999840
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{15999840}=\sqrt{144*111110}=\sqrt{144}*\sqrt{111110}=12\sqrt{111110}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4000)-12\sqrt{111110}}{2*8}=\frac{4000-12\sqrt{111110}}{16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4000)+12\sqrt{111110}}{2*8}=\frac{4000+12\sqrt{111110}}{16}
$