1/2x+5=2/5x-8

Solution for 1/2x+5=2/5x-8 equation:

1/2x+5=2/5x-8

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x-8)!=0

x∈R


We get rid of parentheses

1/2x-2/5x+8+5=0

We calculate fractions


5x/10x^2+(-4x)/10x^2+8+5=0

We add all the numbers together, and all the variables

5x/10x^2+(-4x)/10x^2+13=0

We multiply all the terms by the denominator


5x+(-4x)+13*10x^2=0

Wy multiply elements

130x^2+5x+(-4x)=0

We get rid of parentheses

130x^2+5x-4x=0

We add all the numbers together, and all the variables

130x^2+x=0

a = 130; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·130·0
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*130}=\frac{-2}{260}
=-1/130
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*130}=\frac{0}{260}
=0
$