1/3x-5=2x+4

Solution for 1/3x-5=2x+4 equation:

1/3x-5=2x+4

We move all terms to the left:

1/3x-5-(2x+4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-2x-4-5=0

We multiply all the terms by the denominator


-2x*3x-4*3x-5*3x+1=0

Wy multiply elements

-6x^2-12x-15x+1=0

We add all the numbers together, and all the variables

-6x^2-27x+1=0

a = -6; b = -27; c = +1;
Δ = b2-4ac
Δ = -272-4·(-6)·1
Δ = 753
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{-(-27)-\sqrt{753}}{2*-6}=\frac{27-\sqrt{753}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{753}}{2*-6}=\frac{27+\sqrt{753}}{-12}
$