X-1/3x-4=12

Solution for X-1/3x-4=12 equation:

X-1/3X-4=12

We move all terms to the left:

X-1/3X-4-(12)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

X-1/3X-16=0

We multiply all the terms by the denominator


X*3X-16*3X-1=0

Wy multiply elements

3X^2-48X-1=0

a = 3; b = -48; c = -1;
Δ = b2-4ac
Δ = -482-4·3·(-1)
Δ = 2316
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2316}=\sqrt{4*579}=\sqrt{4}*\sqrt{579}=2\sqrt{579}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{579}}{2*3}=\frac{48-2\sqrt{579}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{579}}{2*3}=\frac{48+2\sqrt{579}}{6}
$