9f=(1/2)(12f-2)

Solution for 9f=(1/2)(12f-2) equation:

9f=(1/2)(12f-2)

We move all terms to the left:

9f-((1/2)(12f-2))=0


Domain of the equation: 2)(12f-2))!=0

f∈R


We add all the numbers together, and all the variables

9f-((+1/2)(12f-2))=0

We multiply parentheses ..

-((+12f^2+1/2*-2))+9f=0

We multiply all the terms by the denominator


-((+12f^2+1+9f*2*-2))=0


We calculate terms in parentheses: -((+12f^2+1+9f*2*-2)), so:

(+12f^2+1+9f*2*-2)

We get rid of parentheses

12f^2+9f*2*+1-2

We add all the numbers together, and all the variables

12f^2+9f*2*-1

Wy multiply elements

12f^2+18f^2-1

We add all the numbers together, and all the variables

30f^2-1

Back to the equation:

-(30f^2-1)


We get rid of parentheses

-30f^2+1=0

a = -30; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-30)·1
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*-30}=\frac{0-2\sqrt{30}}{-60}
=-\frac{2\sqrt{30}}{-60}
=-\frac{\sqrt{30}}{-30}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*-30}=\frac{0+2\sqrt{30}}{-60}
=\frac{2\sqrt{30}}{-60}
=\frac{\sqrt{30}}{-30}
$