1/3f+12f=360

Solution for 1/3f+12f=360 equation:

1/3f+12f=360

We move all terms to the left:

1/3f+12f-(360)=0


Domain of the equation: 3f!=0

f!=0/3

f!=0

f∈R


We add all the numbers together, and all the variables

12f+1/3f-360=0

We multiply all the terms by the denominator


12f*3f-360*3f+1=0

Wy multiply elements

36f^2-1080f+1=0

a = 36; b = -1080; c = +1;
Δ = b2-4ac
Δ = -10802-4·36·1
Δ = 1166256
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:

$\sqrt{\Delta}=\sqrt{1166256}=\sqrt{144*8099}=\sqrt{144}*\sqrt{8099}=12\sqrt{8099}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1080)-12\sqrt{8099}}{2*36}=\frac{1080-12\sqrt{8099}}{72}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1080)+12\sqrt{8099}}{2*36}=\frac{1080+12\sqrt{8099}}{72}
$