1/2x+13=3/5x-3

Solution for 1/2x+13=3/5x-3 equation:

1/2x+13=3/5x-3

We move all terms to the left:

1/2x+13-(3/5x-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-3/5x+3+13=0

We calculate fractions


5x/10x^2+(-6x)/10x^2+3+13=0

We add all the numbers together, and all the variables

5x/10x^2+(-6x)/10x^2+16=0

We multiply all the terms by the denominator


5x+(-6x)+16*10x^2=0

Wy multiply elements

160x^2+5x+(-6x)=0

We get rid of parentheses

160x^2+5x-6x=0

We add all the numbers together, and all the variables

160x^2-1x=0

a = 160; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·160·0
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*160}=\frac{0}{320}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*160}=\frac{2}{320}
=1/160
$