1/4x=2/5x+2

Solution for 1/4x=2/5x+2 equation:

1/4x=2/5x+2

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x+2)!=0

x∈R


We get rid of parentheses

1/4x-2/5x-2=0

We calculate fractions


5x/20x^2+(-8x)/20x^2-2=0

We multiply all the terms by the denominator


5x+(-8x)-2*20x^2=0

Wy multiply elements

-40x^2+5x+(-8x)=0

We get rid of parentheses

-40x^2+5x-8x=0

We add all the numbers together, and all the variables

-40x^2-3x=0

a = -40; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-40)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-40}=\frac{0}{-80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-40}=\frac{6}{-80}
=-3/40
$