12+12/1x=3x

Solution for 12+12/1x=3x equation:

12+12/1x=3x

We move all terms to the left:

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


Domain of the equation: 1x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-3x^2+12x+12=0

a = -3; b = 12; c = +12;
Δ = b2-4ac
Δ = 122-4·(-3)·12
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{2}}{2*-3}=\frac{-12-12\sqrt{2}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{2}}{2*-3}=\frac{-12+12\sqrt{2}}{-6}
$