-7/20f+2/5=1/4f

Solution for -7/20f+2/5=1/4f equation:

-7/20f+2/5=1/4f

We move all terms to the left:

-7/20f+2/5-(1/4f)=0


Domain of the equation: 20f!=0

f!=0/20

f!=0

f∈R



Domain of the equation: 4f)!=0

f!=0/1

f!=0

f∈R


We add all the numbers together, and all the variables

-7/20f-(+1/4f)+2/5=0

We get rid of parentheses

-7/20f-1/4f+2/5=0

We calculate fractions


640f^2/2000f^2+(-700f)/2000f^2+(-500f)/2000f^2=0

We multiply all the terms by the denominator


640f^2+(-700f)+(-500f)=0

We get rid of parentheses

640f^2-700f-500f=0

We add all the numbers together, and all the variables

640f^2-1200f=0

a = 640; b = -1200; c = 0;
Δ = b2-4ac
Δ = -12002-4·640·0
Δ = 1440000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1440000}=1200$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1200)-1200}{2*640}=\frac{0}{1280}
=0
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1200)+1200}{2*640}=\frac{2400}{1280}
=1+7/8
$