1/2x+2=2/5x+3

Solution for 1/2x+2=2/5x+3 equation:

1/2x+2=2/5x+3

We move all terms to the left:

1/2x+2-(2/5x+3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x+3)!=0

x∈R


We get rid of parentheses

1/2x-2/5x-3+2=0

We calculate fractions


5x/10x^2+(-4x)/10x^2-3+2=0

We add all the numbers together, and all the variables

5x/10x^2+(-4x)/10x^2-1=0

We multiply all the terms by the denominator


5x+(-4x)-1*10x^2=0

Wy multiply elements

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

We get rid of parentheses

-10x^2+5x-4x=0

We add all the numbers together, and all the variables

-10x^2+x=0

a = -10; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-10)·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*-10}=\frac{-2}{-20}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-10}=\frac{0}{-20}
=0
$