2/f=5-2f

Solution for 2/f=5-2f equation:

2/f=5-2f

We move all terms to the left:

2/f-(5-2f)=0


Domain of the equation: f!=0

f∈R


We add all the numbers together, and all the variables

2/f-(-2f+5)=0

We get rid of parentheses

2/f+2f-5=0

We multiply all the terms by the denominator


2f*f-5*f+2=0

We add all the numbers together, and all the variables

-5f+2f*f+2=0

Wy multiply elements

2f^2-5f+2=0

a = 2; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·2·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*2}=\frac{2}{4}
=1/2
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*2}=\frac{8}{4}
=2
$