x+x2/3=180

Solution for x+x2/3=180 equation:

x+x2/3=180

We move all terms to the left:

x+x2/3-(180)=0

We multiply all the terms by the denominator


x*3+x2-180*3=0

We add all the numbers together, and all the variables

x^2+x*3-540=0

Wy multiply elements

x^2+3x-540=0

a = 1; b = 3; c = -540;
Δ = b2-4ac
Δ = 32-4·1·(-540)
Δ = 2169
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:

$\sqrt{\Delta}=\sqrt{2169}=\sqrt{9*241}=\sqrt{9}*\sqrt{241}=3\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{241}}{2*1}=\frac{-3-3\sqrt{241}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{241}}{2*1}=\frac{-3+3\sqrt{241}}{2}
$