1/3x-12=100-x

Solution for 1/3x-12=100-x equation:

1/3x-12=100-x

We move all terms to the left:

1/3x-12-(100-x)=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+100)-12=0

We get rid of parentheses

1/3x+1x-100-12=0

We multiply all the terms by the denominator


1x*3x-100*3x-12*3x+1=0

Wy multiply elements

3x^2-300x-36x+1=0

We add all the numbers together, and all the variables

3x^2-336x+1=0

a = 3; b = -336; c = +1;
Δ = b2-4ac
Δ = -3362-4·3·1
Δ = 112884
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:

$\sqrt{\Delta}=\sqrt{112884}=\sqrt{4*28221}=\sqrt{4}*\sqrt{28221}=2\sqrt{28221}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-336)-2\sqrt{28221}}{2*3}=\frac{336-2\sqrt{28221}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-336)+2\sqrt{28221}}{2*3}=\frac{336+2\sqrt{28221}}{6}
$