2/4x-7/5x=4/10

Solution for 2/4x-7/5x=4/10 equation:

2/4x-7/5x=4/10

We move all terms to the left:

2/4x-7/5x-(4/10)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

2/4x-7/5x-(+4/10)=0

We get rid of parentheses

2/4x-7/5x-4/10=0

We calculate fractions


(-400x^2)/200x^2+100x/200x^2+(-280x)/200x^2=0

We multiply all the terms by the denominator


(-400x^2)+100x+(-280x)=0

We get rid of parentheses

-400x^2+100x-280x=0

We add all the numbers together, and all the variables

-400x^2-180x=0

a = -400; b = -180; c = 0;
Δ = b2-4ac
Δ = -1802-4·(-400)·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-180}{2*-400}=\frac{0}{-800}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+180}{2*-400}=\frac{360}{-800}
=-9/20
$