x+2/3x+5x=360

Solution for x+2/3x+5x=360 equation:

x+2/3x+5x=360

We move all terms to the left:

x+2/3x+5x-(360)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

6x+2/3x-360=0

We multiply all the terms by the denominator


6x*3x-360*3x+2=0

Wy multiply elements

18x^2-1080x+2=0

a = 18; b = -1080; c = +2;
Δ = b2-4ac
Δ = -10802-4·18·2
Δ = 1166256
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:

$\sqrt{\Delta}=\sqrt{1166256}=\sqrt{144*8099}=\sqrt{144}*\sqrt{8099}=12\sqrt{8099}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1080)-12\sqrt{8099}}{2*18}=\frac{1080-12\sqrt{8099}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1080)+12\sqrt{8099}}{2*18}=\frac{1080+12\sqrt{8099}}{36}
$