X+1/3x+2/3x=180

Solution for X+1/3x+2/3x=180 equation:

X+1/3X+2/3X=180

We move all terms to the left:

X+1/3X+2/3X-(180)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-180*3X+1+2=0

We add all the numbers together, and all the variables

X*3X-180*3X+3=0

Wy multiply elements

3X^2-540X+3=0

a = 3; b = -540; c = +3;
Δ = b2-4ac
Δ = -5402-4·3·3
Δ = 291564
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:

$\sqrt{\Delta}=\sqrt{291564}=\sqrt{36*8099}=\sqrt{36}*\sqrt{8099}=6\sqrt{8099}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-6\sqrt{8099}}{2*3}=\frac{540-6\sqrt{8099}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+6\sqrt{8099}}{2*3}=\frac{540+6\sqrt{8099}}{6}
$