X+1/3x+2/3x=360

Solution for X+1/3x+2/3x=360 equation:

X+1/3X+2/3X=360

We move all terms to the left:

X+1/3X+2/3X-(360)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-360*3X+1+2=0

We add all the numbers together, and all the variables

X*3X-360*3X+3=0

Wy multiply elements

3X^2-1080X+3=0

a = 3; b = -1080; c = +3;
Δ = b2-4ac
Δ = -10802-4·3·3
Δ = 1166364
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:

$\sqrt{\Delta}=\sqrt{1166364}=\sqrt{36*32399}=\sqrt{36}*\sqrt{32399}=6\sqrt{32399}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1080)-6\sqrt{32399}}{2*3}=\frac{1080-6\sqrt{32399}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1080)+6\sqrt{32399}}{2*3}=\frac{1080+6\sqrt{32399}}{6}
$