3x-12x+1/6x-4x=0

Solution for 3x-12x+1/6x-4x=0 equation:

3x-12x+1/6x-4x=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-13x+1/6x=0

We multiply all the terms by the denominator


-13x*6x+1=0

Wy multiply elements

-78x^2+1=0

a = -78; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-78)·1
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{78}}{2*-78}=\frac{0-2\sqrt{78}}{-156}
=-\frac{2\sqrt{78}}{-156}
=-\frac{\sqrt{78}}{-78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{78}}{2*-78}=\frac{0+2\sqrt{78}}{-156}
=\frac{2\sqrt{78}}{-156}
=\frac{\sqrt{78}}{-78}
$