1/2x-5=3/5x+8

Solution for 1/2x-5=3/5x+8 equation:

1/2x-5=3/5x+8

We move all terms to the left:

1/2x-5-(3/5x+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-3/5x-8-5=0

We calculate fractions


5x/10x^2+(-6x)/10x^2-8-5=0

We add all the numbers together, and all the variables

5x/10x^2+(-6x)/10x^2-13=0

We multiply all the terms by the denominator


5x+(-6x)-13*10x^2=0

Wy multiply elements

-130x^2+5x+(-6x)=0

We get rid of parentheses

-130x^2+5x-6x=0

We add all the numbers together, and all the variables

-130x^2-1x=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{0}{-260}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-130}=\frac{2}{-260}
=-1/130
$