6-1/4f=f-3

Solution for 6-1/4f=f-3 equation:

6-1/4f=f-3

We move all terms to the left:

6-1/4f-(f-3)=0


Domain of the equation: 4f!=0

f!=0/4

f!=0

f∈R


We get rid of parentheses

-1/4f-f+3+6=0

We multiply all the terms by the denominator


-f*4f+3*4f+6*4f-1=0

Wy multiply elements

-4f^2+12f+24f-1=0

We add all the numbers together, and all the variables

-4f^2+36f-1=0

a = -4; b = 36; c = -1;
Δ = b2-4ac
Δ = 362-4·(-4)·(-1)
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-16\sqrt{5}}{2*-4}=\frac{-36-16\sqrt{5}}{-8}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+16\sqrt{5}}{2*-4}=\frac{-36+16\sqrt{5}}{-8}
$