-2/5x+3/20x=5

Solution for -2/5x+3/20x=5 equation:

-2/5x+3/20x=5

We move all terms to the left:

-2/5x+3/20x-(5)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 20x!=0

x!=0/20

x!=0

x∈R


We calculate fractions


(-40x)/100x^2+15x/100x^2-5=0

We multiply all the terms by the denominator


(-40x)+15x-5*100x^2=0

We add all the numbers together, and all the variables

15x+(-40x)-5*100x^2=0

Wy multiply elements

-500x^2+15x+(-40x)=0

We get rid of parentheses

-500x^2+15x-40x=0

We add all the numbers together, and all the variables

-500x^2-25x=0

a = -500; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·(-500)·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*-500}=\frac{0}{-1000}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*-500}=\frac{50}{-1000}
=-1/20
$