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

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

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

We move all terms to the left:

1/4x+1-(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+1=0

We calculate fractions


5x/20x^2+(-8x)/20x^2+2+1=0

We add all the numbers together, and all the variables

5x/20x^2+(-8x)/20x^2+3=0

We multiply all the terms by the denominator


5x+(-8x)+3*20x^2=0

Wy multiply elements

60x^2+5x+(-8x)=0

We get rid of parentheses

60x^2+5x-8x=0

We add all the numbers together, and all the variables

60x^2-3x=0

a = 60; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·60·0
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*60}=\frac{0}{120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*60}=\frac{6}{120}
=1/20
$