(3/12x)+(8/12x)+50=x

Solution for (3/12x)+(8/12x)+50=x equation:

(3/12x)+(8/12x)+50=x

We move all terms to the left:

(3/12x)+(8/12x)+50-(x)=0


Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3/12x)+(+8/12x)-x+50=0

We add all the numbers together, and all the variables

-1x+(+3/12x)+(+8/12x)+50=0

We get rid of parentheses

-1x+3/12x+8/12x+50=0

We multiply all the terms by the denominator


-1x*12x+50*12x+3+8=0

We add all the numbers together, and all the variables

-1x*12x+50*12x+11=0

Wy multiply elements

-12x^2+600x+11=0

a = -12; b = 600; c = +11;
Δ = b2-4ac
Δ = 6002-4·(-12)·11
Δ = 360528
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:

$\sqrt{\Delta}=\sqrt{360528}=\sqrt{16*22533}=\sqrt{16}*\sqrt{22533}=4\sqrt{22533}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(600)-4\sqrt{22533}}{2*-12}=\frac{-600-4\sqrt{22533}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(600)+4\sqrt{22533}}{2*-12}=\frac{-600+4\sqrt{22533}}{-24}
$