f-4=6/2f+6

Solution for f-4=6/2f+6 equation:

f-4=6/2f+6

We move all terms to the left:

f-4-(6/2f+6)=0


Domain of the equation: 2f+6)!=0

f∈R


We get rid of parentheses

f-6/2f-6-4=0

We multiply all the terms by the denominator


f*2f-6*2f-4*2f-6=0

Wy multiply elements

2f^2-12f-8f-6=0

We add all the numbers together, and all the variables

2f^2-20f-6=0

a = 2; b = -20; c = -6;
Δ = b2-4ac
Δ = -202-4·2·(-6)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{7}}{2*2}=\frac{20-8\sqrt{7}}{4}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{7}}{2*2}=\frac{20+8\sqrt{7}}{4}
$