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

Solution for 3/4f+2-1/2f=0 equation:

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


Domain of the equation: 4f!=0

f!=0/4

f!=0

f∈R



Domain of the equation: 2f!=0

f!=0/2

f!=0

f∈R


We calculate fractions


6f/8f^2+(-4f)/8f^2+2=0

We multiply all the terms by the denominator


6f+(-4f)+2*8f^2=0

Wy multiply elements

16f^2+6f+(-4f)=0

We get rid of parentheses

16f^2+6f-4f=0

We add all the numbers together, and all the variables

16f^2+2f=0

a = 16; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·16·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*16}=\frac{-4}{32}
=-1/8
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*16}=\frac{0}{32}
=0
$