1/21*f=13

Solution for 1/21*f=13 equation:

1/21*f=13

We move all terms to the left:

1/21*f-(13)=0


Domain of the equation: 21*f!=0

f!=0/1

f!=0

f∈R


We multiply all the terms by the denominator


-13*21*f+1=0

Wy multiply elements

-273f*f+1=0

Wy multiply elements

-273f^2+1=0

a = -273; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-273)·1
Δ = 1092
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:

$\sqrt{\Delta}=\sqrt{1092}=\sqrt{4*273}=\sqrt{4}*\sqrt{273}=2\sqrt{273}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{273}}{2*-273}=\frac{0-2\sqrt{273}}{-546}
=-\frac{2\sqrt{273}}{-546}
=-\frac{\sqrt{273}}{-273}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{273}}{2*-273}=\frac{0+2\sqrt{273}}{-546}
=\frac{2\sqrt{273}}{-546}
=\frac{\sqrt{273}}{-273}
$