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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

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

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

We calculate fractions


(-560x^2)/800x^2+(-320x)/800x^2+200x/800x^2+40=0

We multiply all the terms by the denominator


(-560x^2)+(-320x)+200x+40*800x^2=0

We add all the numbers together, and all the variables

(-560x^2)+200x+(-320x)+40*800x^2=0

Wy multiply elements

(-560x^2)+32000x^2+200x+(-320x)=0

We get rid of parentheses

-560x^2+32000x^2+200x-320x=0

We add all the numbers together, and all the variables

31440x^2-120x=0

a = 31440; b = -120; c = 0;
Δ = b2-4ac
Δ = -1202-4·31440·0
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-120}{2*31440}=\frac{0}{62880}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+120}{2*31440}=\frac{240}{62880}
=1/262
$