2/3x+x=180

Solution for 2/3x+x=180 equation:

2/3x+x=180

We move all terms to the left:

2/3x+x-(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+2/3x-180=0

We multiply all the terms by the denominator


x*3x-180*3x+2=0

Wy multiply elements

3x^2-540x+2=0

a = 3; b = -540; c = +2;
Δ = b2-4ac
Δ = -5402-4·3·2
Δ = 291576
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:

$\sqrt{\Delta}=\sqrt{291576}=\sqrt{4*72894}=\sqrt{4}*\sqrt{72894}=2\sqrt{72894}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-2\sqrt{72894}}{2*3}=\frac{540-2\sqrt{72894}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+2\sqrt{72894}}{2*3}=\frac{540+2\sqrt{72894}}{6}
$