6/f=2.5f=

Solution for 6/f=2.5f= equation:

6/f=2.5f=

We move all terms to the left:

6/f-(2.5f)=0


Domain of the equation: f!=0

f∈R


We add all the numbers together, and all the variables

6/f-(+2.5f)=0

We get rid of parentheses

6/f-2.5f=0

We multiply all the terms by the denominator


-(2.5f)*f+6=0

We add all the numbers together, and all the variables

-(+2.5f)*f+6=0

We multiply parentheses

-2f^2+6=0

a = -2; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-2)·6
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*-2}=\frac{0-4\sqrt{3}}{-4}
=-\frac{4\sqrt{3}}{-4}
=-\frac{\sqrt{3}}{-1}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*-2}=\frac{0+4\sqrt{3}}{-4}
=\frac{4\sqrt{3}}{-4}
=\frac{\sqrt{3}}{-1}
$