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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x+4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


5x+(-4x)-2*10x^2=0

Wy multiply elements

-20x^2+5x+(-4x)=0

We get rid of parentheses

-20x^2+5x-4x=0

We add all the numbers together, and all the variables

-20x^2+x=0

a = -20; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-20)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-20}=\frac{-2}{-40}
=1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-20}=\frac{0}{-40}
=0
$