7f-12/3f-1=5

Solution for 7f-12/3f-1=5 equation:

7f-12/3f-1=5

We move all terms to the left:

7f-12/3f-1-(5)=0


Domain of the equation: 3f!=0

f!=0/3

f!=0

f∈R


We add all the numbers together, and all the variables

7f-12/3f-6=0

We multiply all the terms by the denominator


7f*3f-6*3f-12=0

Wy multiply elements

21f^2-18f-12=0

a = 21; b = -18; c = -12;
Δ = b2-4ac
Δ = -182-4·21·(-12)
Δ = 1332
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:

$\sqrt{\Delta}=\sqrt{1332}=\sqrt{36*37}=\sqrt{36}*\sqrt{37}=6\sqrt{37}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{37}}{2*21}=\frac{18-6\sqrt{37}}{42}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{37}}{2*21}=\frac{18+6\sqrt{37}}{42}
$