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

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

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

We move all terms to the left:

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

We calculate fractions


125x/250x^2+(-4x)/250x^2+(-6x)/250x^2-3=0

We multiply all the terms by the denominator


125x+(-4x)+(-6x)-3*250x^2=0

Wy multiply elements

-750x^2+125x+(-4x)+(-6x)=0

We get rid of parentheses

-750x^2+125x-4x-6x=0

We add all the numbers together, and all the variables

-750x^2+115x=0

a = -750; b = 115; c = 0;
Δ = b2-4ac
Δ = 1152-4·(-750)·0
Δ = 13225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13225}=115$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(115)-115}{2*-750}=\frac{-230}{-1500}
=23/150
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(115)+115}{2*-750}=\frac{0}{-1500}
=0
$