-4x=1/3x-6

Solution for -4x=1/3x-6 equation:

-4x=1/3x-6

We move all terms to the left:

-4x-(1/3x-6)=0


Domain of the equation: 3x-6)!=0

x∈R


We get rid of parentheses

-4x-1/3x+6=0

We multiply all the terms by the denominator


-4x*3x+6*3x-1=0

Wy multiply elements

-12x^2+18x-1=0

a = -12; b = 18; c = -1;
Δ = b2-4ac
Δ = 182-4·(-12)·(-1)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{69}}{2*-12}=\frac{-18-2\sqrt{69}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{69}}{2*-12}=\frac{-18+2\sqrt{69}}{-24}
$