2/5x+1/10x-1/20=18

Solution for 2/5x+1/10x-1/20=18 equation:

2/5x+1/10x-1/20=18

We move all terms to the left:

2/5x+1/10x-1/20-(18)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


determiningTheFunctionDomain
2/5x+1/10x-18-1/20=0

We calculate fractions


(-50x^2)/2000x^2+800x/2000x^2+200x/2000x^2-18=0

We multiply all the terms by the denominator


(-50x^2)+800x+200x-18*2000x^2=0

We add all the numbers together, and all the variables

(-50x^2)+1000x-18*2000x^2=0

Wy multiply elements

(-50x^2)-36000x^2+1000x=0

We get rid of parentheses

-50x^2-36000x^2+1000x=0

We add all the numbers together, and all the variables

-36050x^2+1000x=0

a = -36050; b = 1000; c = 0;
Δ = b2-4ac
Δ = 10002-4·(-36050)·0
Δ = 1000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1000000}=1000$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1000)-1000}{2*-36050}=\frac{-2000}{-72100}
=20/721
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1000)+1000}{2*-36050}=\frac{0}{-72100}
=0
$