-2/5-7/20x+1/4x=-40

Solution for -2/5-7/20x+1/4x=-40 equation:

-2/5-7/20x+1/4x=-40

We move all terms to the left:

-2/5-7/20x+1/4x-(-40)=0


Domain of the equation: 20x!=0

x!=0/20

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-7/20x+1/4x+40-2/5=0

We calculate fractions


(-640x^2)/2000x^2+(-700x)/2000x^2+500x/2000x^2+40=0

We multiply all the terms by the denominator


(-640x^2)+(-700x)+500x+40*2000x^2=0

We add all the numbers together, and all the variables

(-640x^2)+500x+(-700x)+40*2000x^2=0

Wy multiply elements

(-640x^2)+80000x^2+500x+(-700x)=0

We get rid of parentheses

-640x^2+80000x^2+500x-700x=0

We add all the numbers together, and all the variables

79360x^2-200x=0

a = 79360; b = -200; c = 0;
Δ = b2-4ac
Δ = -2002-4·79360·0
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-200}{2*79360}=\frac{0}{158720}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+200}{2*79360}=\frac{400}{158720}
=5/1984
$