30=3f+1/2f=9

Solution for 30=3f+1/2f=9 equation:

30=3f+1/2f=9

We move all terms to the left:

30-(3f+1/2f)=0


Domain of the equation: 2f)!=0

f!=0/1

f!=0

f∈R


We add all the numbers together, and all the variables

-(+3f+1/2f)+30=0

We get rid of parentheses

-3f-1/2f+30=0

We multiply all the terms by the denominator


-3f*2f+30*2f-1=0

Wy multiply elements

-6f^2+60f-1=0

a = -6; b = 60; c = -1;
Δ = b2-4ac
Δ = 602-4·(-6)·(-1)
Δ = 3576
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:

$\sqrt{\Delta}=\sqrt{3576}=\sqrt{4*894}=\sqrt{4}*\sqrt{894}=2\sqrt{894}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{894}}{2*-6}=\frac{-60-2\sqrt{894}}{-12}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{894}}{2*-6}=\frac{-60+2\sqrt{894}}{-12}
$