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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

60x^2+(-2x)+(-3x)=0

We get rid of parentheses

60x^2-2x-3x=0

We add all the numbers together, and all the variables

60x^2-5x=0

a = 60; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·60·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*60}=\frac{0}{120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*60}=\frac{10}{120}
=1/12
$