1/6x+2/3=1/4x-13

Solution for 1/6x+2/3=1/4x-13 equation:

1/6x+2/3=1/4x-13

We move all terms to the left:

1/6x+2/3-(1/4x-13)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 4x-13)!=0

x∈R


We get rid of parentheses

1/6x-1/4x+13+2/3=0

We calculate fractions


192x^2/216x^2+36x/216x^2+(-54x)/216x^2+13=0

We multiply all the terms by the denominator


192x^2+36x+(-54x)+13*216x^2=0

Wy multiply elements

192x^2+2808x^2+36x+(-54x)=0

We get rid of parentheses

192x^2+2808x^2+36x-54x=0

We add all the numbers together, and all the variables

3000x^2-18x=0

a = 3000; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·3000·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*3000}=\frac{0}{6000}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*3000}=\frac{36}{6000}
=3/500
$