1/3x+x=160

Solution for 1/3x+x=160 equation:

1/3x+x=160

We move all terms to the left:

1/3x+x-(160)=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-160=0

We multiply all the terms by the denominator


x*3x-160*3x+1=0

Wy multiply elements

3x^2-480x+1=0

a = 3; b = -480; c = +1;
Δ = b2-4ac
Δ = -4802-4·3·1
Δ = 230388
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:

$\sqrt{\Delta}=\sqrt{230388}=\sqrt{4*57597}=\sqrt{4}*\sqrt{57597}=2\sqrt{57597}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-2\sqrt{57597}}{2*3}=\frac{480-2\sqrt{57597}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+2\sqrt{57597}}{2*3}=\frac{480+2\sqrt{57597}}{6}
$