1/3x+4=12x-2

Solution for 1/3x+4=12x-2 equation:

1/3x+4=12x-2

We move all terms to the left:

1/3x+4-(12x-2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-12x+2+4=0

We multiply all the terms by the denominator


-12x*3x+2*3x+4*3x+1=0

Wy multiply elements

-36x^2+6x+12x+1=0

We add all the numbers together, and all the variables

-36x^2+18x+1=0

a = -36; b = 18; c = +1;
Δ = b2-4ac
Δ = 182-4·(-36)·1
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{13}}{2*-36}=\frac{-18-6\sqrt{13}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{13}}{2*-36}=\frac{-18+6\sqrt{13}}{-72}
$