(600/f)+40=f

Solution for (600/f)+40=f equation:

(600/f)+40=f

We move all terms to the left:

(600/f)+40-(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

(+600/f)-f+40=0

We add all the numbers together, and all the variables

-1f+(+600/f)+40=0

We get rid of parentheses

-1f+600/f+40=0

We multiply all the terms by the denominator


-1f*f+40*f+600=0

We add all the numbers together, and all the variables

40f-1f*f+600=0

Wy multiply elements

-1f^2+40f+600=0

a = -1; b = 40; c = +600;
Δ = b2-4ac
Δ = 402-4·(-1)·600
Δ = 4000
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:

$\sqrt{\Delta}=\sqrt{4000}=\sqrt{400*10}=\sqrt{400}*\sqrt{10}=20\sqrt{10}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-20\sqrt{10}}{2*-1}=\frac{-40-20\sqrt{10}}{-2}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+20\sqrt{10}}{2*-1}=\frac{-40+20\sqrt{10}}{-2}
$