13=1/3x-4x

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

13=1/3x-4x

We move all terms to the left:

13-(1/3x-4x)=0


Domain of the equation: 3x-4x)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

4x-1/3x+13=0

We multiply all the terms by the denominator


4x*3x+13*3x-1=0

Wy multiply elements

12x^2+39x-1=0

a = 12; b = 39; c = -1;
Δ = b2-4ac
Δ = 392-4·12·(-1)
Δ = 1569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-\sqrt{1569}}{2*12}=\frac{-39-\sqrt{1569}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+\sqrt{1569}}{2*12}=\frac{-39+\sqrt{1569}}{24}
$