1/12x+15-12x=6x+12

Solution for 1/12x+15-12x=6x+12 equation:

1/12x+15-12x=6x+12

We move all terms to the left:

1/12x+15-12x-(6x+12)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We add all the numbers together, and all the variables

-12x+1/12x-(6x+12)+15=0

We get rid of parentheses

-12x+1/12x-6x-12+15=0

We multiply all the terms by the denominator


-12x*12x-6x*12x-12*12x+15*12x+1=0

Wy multiply elements

-144x^2-72x^2-144x+180x+1=0

We add all the numbers together, and all the variables

-216x^2+36x+1=0

a = -216; b = 36; c = +1;
Δ = b2-4ac
Δ = 362-4·(-216)·1
Δ = 2160
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:

$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12\sqrt{15}}{2*-216}=\frac{-36-12\sqrt{15}}{-432}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12\sqrt{15}}{2*-216}=\frac{-36+12\sqrt{15}}{-432}
$