2-1/4f=f-3/4f+3

Solution for 2-1/4f=f-3/4f+3 equation:

2-1/4f=f-3/4f+3

We move all terms to the left:

2-1/4f-(f-3/4f+3)=0


Domain of the equation: 4f!=0

f!=0/4

f!=0

f∈R



Domain of the equation: 4f+3)!=0

f∈R


We get rid of parentheses

-1/4f-f+3/4f-3+2=0

We multiply all the terms by the denominator


-f*4f-3*4f+2*4f-1+3=0

We add all the numbers together, and all the variables

-f*4f-3*4f+2*4f+2=0

Wy multiply elements

-4f^2-12f+8f+2=0

We add all the numbers together, and all the variables

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

a = -4; b = -4; c = +2;
Δ = b2-4ac
Δ = -42-4·(-4)·2
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{3}}{2*-4}=\frac{4-4\sqrt{3}}{-8}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{3}}{2*-4}=\frac{4+4\sqrt{3}}{-8}
$