x+(1/3x)=80

Solution for x+(1/3x)=80 equation:

x+(1/3x)=80

We move all terms to the left:

x+(1/3x)-(80)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+(+1/3x)-80=0

We get rid of parentheses

x+1/3x-80=0

We multiply all the terms by the denominator


x*3x-80*3x+1=0

Wy multiply elements

3x^2-240x+1=0

a = 3; b = -240; c = +1;
Δ = b2-4ac
Δ = -2402-4·3·1
Δ = 57588
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:

$\sqrt{\Delta}=\sqrt{57588}=\sqrt{4*14397}=\sqrt{4}*\sqrt{14397}=2\sqrt{14397}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-2\sqrt{14397}}{2*3}=\frac{240-2\sqrt{14397}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+2\sqrt{14397}}{2*3}=\frac{240+2\sqrt{14397}}{6}
$