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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


5x/10x^2+(-6x)/10x^2+1+3=0

We add all the numbers together, and all the variables

5x/10x^2+(-6x)/10x^2+4=0

We multiply all the terms by the denominator


5x+(-6x)+4*10x^2=0

Wy multiply elements

40x^2+5x+(-6x)=0

We get rid of parentheses

40x^2+5x-6x=0

We add all the numbers together, and all the variables

40x^2-1x=0

a = 40; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·40·0
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*40}=\frac{0}{80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*40}=\frac{2}{80}
=1/40
$