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

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

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

We move all terms to the left:

1/5x-3-(-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

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

7x-6*10x^2=0

Wy multiply elements

-60x^2+7x=0

a = -60; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-60)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-60}=\frac{-14}{-120}
=7/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-60}=\frac{0}{-120}
=0
$