1/3x-8=12-1x

Solution for 1/3x-8=12-1x equation:

1/3x-8=12-1x

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2-36x-24x+1=0

We add all the numbers together, and all the variables

3x^2-60x+1=0

a = 3; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·3·1
Δ = 3588
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:

$\sqrt{\Delta}=\sqrt{3588}=\sqrt{4*897}=\sqrt{4}*\sqrt{897}=2\sqrt{897}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{897}}{2*3}=\frac{60-2\sqrt{897}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{897}}{2*3}=\frac{60+2\sqrt{897}}{6}
$