1/3x+x=1348

Solution for 1/3x+x=1348 equation:

1/3x+x=1348

We move all terms to the left:

1/3x+x-(1348)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/3x-1348=0

We multiply all the terms by the denominator


x*3x-1348*3x+1=0

Wy multiply elements

3x^2-4044x+1=0

a = 3; b = -4044; c = +1;
Δ = b2-4ac
Δ = -40442-4·3·1
Δ = 16353924
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:

$\sqrt{\Delta}=\sqrt{16353924}=\sqrt{4*4088481}=\sqrt{4}*\sqrt{4088481}=2\sqrt{4088481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4044)-2\sqrt{4088481}}{2*3}=\frac{4044-2\sqrt{4088481}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4044)+2\sqrt{4088481}}{2*3}=\frac{4044+2\sqrt{4088481}}{6}
$