1/3x+x=60

Solution for 1/3x+x=60 equation:

1/3x+x=60

We move all terms to the left:

1/3x+x-(60)=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-60=0

We multiply all the terms by the denominator


x*3x-60*3x+1=0

Wy multiply elements

3x^2-180x+1=0

a = 3; b = -180; c = +1;
Δ = b2-4ac
Δ = -1802-4·3·1
Δ = 32388
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:

$\sqrt{\Delta}=\sqrt{32388}=\sqrt{4*8097}=\sqrt{4}*\sqrt{8097}=2\sqrt{8097}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-2\sqrt{8097}}{2*3}=\frac{180-2\sqrt{8097}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+2\sqrt{8097}}{2*3}=\frac{180+2\sqrt{8097}}{6}
$