1/5x+5=18-1/20x

Solution for 1/5x+5=18-1/20x equation:

1/5x+5=18-1/20x

We move all terms to the left:

1/5x+5-(18-1/20x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 20x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x-(-1/20x+18)+5=0

We get rid of parentheses

1/5x+1/20x-18+5=0

We calculate fractions


20x/100x^2+5x/100x^2-18+5=0

We add all the numbers together, and all the variables

20x/100x^2+5x/100x^2-13=0

We multiply all the terms by the denominator


20x+5x-13*100x^2=0

We add all the numbers together, and all the variables

25x-13*100x^2=0

Wy multiply elements

-1300x^2+25x=0

a = -1300; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-1300)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-1300}=\frac{-50}{-2600}
=1/52
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-1300}=\frac{0}{-2600}
=0
$