x-1/3x=112

Solution for x-1/3x=112 equation:

x-1/3x=112

We move all terms to the left:

x-1/3x-(112)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-112*3x-1=0

Wy multiply elements

3x^2-336x-1=0

a = 3; b = -336; c = -1;
Δ = b2-4ac
Δ = -3362-4·3·(-1)
Δ = 112908
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:

$\sqrt{\Delta}=\sqrt{112908}=\sqrt{37636*3}=\sqrt{37636}*\sqrt{3}=194\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-336)-194\sqrt{3}}{2*3}=\frac{336-194\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-336)+194\sqrt{3}}{2*3}=\frac{336+194\sqrt{3}}{6}
$