1/3x+12-29x=57x+208-5x+38

Solution for 1/3x+12-29x=57x+208-5x+38 equation:

1/3x+12-29x=57x+208-5x+38

We move all terms to the left:

1/3x+12-29x-(57x+208-5x+38)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-29x-(52x+246)+12=0

We add all the numbers together, and all the variables

-29x+1/3x-(52x+246)+12=0

We get rid of parentheses

-29x+1/3x-52x-246+12=0

We multiply all the terms by the denominator


-29x*3x-52x*3x-246*3x+12*3x+1=0

Wy multiply elements

-87x^2-156x^2-738x+36x+1=0

We add all the numbers together, and all the variables

-243x^2-702x+1=0

a = -243; b = -702; c = +1;
Δ = b2-4ac
Δ = -7022-4·(-243)·1
Δ = 493776
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:

$\sqrt{\Delta}=\sqrt{493776}=\sqrt{1296*381}=\sqrt{1296}*\sqrt{381}=36\sqrt{381}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-702)-36\sqrt{381}}{2*-243}=\frac{702-36\sqrt{381}}{-486}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-702)+36\sqrt{381}}{2*-243}=\frac{702+36\sqrt{381}}{-486}
$