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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x-3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-20x^2+6x+(-5x)=0

We get rid of parentheses

-20x^2+6x-5x=0

We add all the numbers together, and all the variables

-20x^2+x=0

a = -20; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-20)·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*-20}=\frac{-2}{-40}
=1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-20}=\frac{0}{-40}
=0
$