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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

11x-5*10x^2=0

Wy multiply elements

-50x^2+11x=0

a = -50; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-50)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-50}=\frac{-22}{-100}
=11/50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-50}=\frac{0}{-100}
=0
$