5/3x+6=13-4x

Solution for 5/3x+6=13-4x equation:

5/3x+6=13-4x

We move all terms to the left:

5/3x+6-(13-4x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5/3x-(-4x+13)+6=0

We get rid of parentheses

5/3x+4x-13+6=0

We multiply all the terms by the denominator


4x*3x-13*3x+6*3x+5=0

Wy multiply elements

12x^2-39x+18x+5=0

We add all the numbers together, and all the variables

12x^2-21x+5=0

a = 12; b = -21; c = +5;
Δ = b2-4ac
Δ = -212-4·12·5
Δ = 201
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{-(-21)-\sqrt{201}}{2*12}=\frac{21-\sqrt{201}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{201}}{2*12}=\frac{21+\sqrt{201}}{24}
$