1/4x+1/5x+1/4=41/20

Solution for 1/4x+1/5x+1/4=41/20 equation:

1/4x+1/5x+1/4=41/20

We move all terms to the left:

1/4x+1/5x+1/4-(41/20)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x+1/5x+1/4-(+41/20)=0

We get rid of parentheses

1/4x+1/5x+1/4-41/20=0

We calculate fractions


(-16400x^2)/6400x^2+200x/6400x^2+1280x/6400x^2+200x/6400x^2=0

We multiply all the terms by the denominator


(-16400x^2)+200x+1280x+200x=0

We add all the numbers together, and all the variables

(-16400x^2)+1680x=0

We get rid of parentheses

-16400x^2+1680x=0

a = -16400; b = 1680; c = 0;
Δ = b2-4ac
Δ = 16802-4·(-16400)·0
Δ = 2822400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2822400}=1680$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1680)-1680}{2*-16400}=\frac{-3360}{-32800}
=21/205
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1680)+1680}{2*-16400}=\frac{0}{-32800}
=0
$