1/5x+5=4-1/4x

Solution for 1/5x+5=4-1/4x equation:

1/5x+5=4-1/4x

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


4x/20x^2+5x/20x^2-4+5=0

We add all the numbers together, and all the variables

4x/20x^2+5x/20x^2+1=0

We multiply all the terms by the denominator


4x+5x+1*20x^2=0

We add all the numbers together, and all the variables

9x+1*20x^2=0

Wy multiply elements

20x^2+9x=0

a = 20; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·20·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*20}=\frac{-18}{40}
=-9/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*20}=\frac{0}{40}
=0
$