7f-12/f=20

Solution for 7f-12/f=20 equation:

7f-12/f=20

We move all terms to the left:

7f-12/f-(20)=0


Domain of the equation: f!=0

f∈R


We multiply all the terms by the denominator


7f*f-20*f-12=0

We add all the numbers together, and all the variables

-20f+7f*f-12=0

Wy multiply elements

7f^2-20f-12=0

a = 7; b = -20; c = -12;
Δ = b2-4ac
Δ = -202-4·7·(-12)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{46}}{2*7}=\frac{20-4\sqrt{46}}{14}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{46}}{2*7}=\frac{20+4\sqrt{46}}{14}
$