1/3x+x+80=180

Solution for 1/3x+x+80=180 equation:

1/3x+x+80=180

We move all terms to the left:

1/3x+x+80-(180)=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-100=0

We multiply all the terms by the denominator


x*3x-100*3x+1=0

Wy multiply elements

3x^2-300x+1=0

a = 3; b = -300; c = +1;
Δ = b2-4ac
Δ = -3002-4·3·1
Δ = 89988
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:

$\sqrt{\Delta}=\sqrt{89988}=\sqrt{4*22497}=\sqrt{4}*\sqrt{22497}=2\sqrt{22497}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-2\sqrt{22497}}{2*3}=\frac{300-2\sqrt{22497}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+2\sqrt{22497}}{2*3}=\frac{300+2\sqrt{22497}}{6}
$