3f-12=3f(f-12)

Solution for 3f-12=3f(f-12) equation:

3f-12=3f(f-12)

We move all terms to the left:

3f-12-(3f(f-12))=0


We calculate terms in parentheses: -(3f(f-12)), so:

3f(f-12)

We multiply parentheses

3f^2-36f

Back to the equation:

-(3f^2-36f)


We get rid of parentheses

-3f^2+3f+36f-12=0

We add all the numbers together, and all the variables

-3f^2+39f-12=0

a = -3; b = 39; c = -12;
Δ = b2-4ac
Δ = 392-4·(-3)·(-12)
Δ = 1377
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:

$\sqrt{\Delta}=\sqrt{1377}=\sqrt{81*17}=\sqrt{81}*\sqrt{17}=9\sqrt{17}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-9\sqrt{17}}{2*-3}=\frac{-39-9\sqrt{17}}{-6}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+9\sqrt{17}}{2*-3}=\frac{-39+9\sqrt{17}}{-6}
$