5/3x+x=360

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

5/3x+x=360

We move all terms to the left:

5/3x+x-(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

x+5/3x-360=0

We multiply all the terms by the denominator


x*3x-360*3x+5=0

Wy multiply elements

3x^2-1080x+5=0

a = 3; b = -1080; c = +5;
Δ = b2-4ac
Δ = -10802-4·3·5
Δ = 1166340
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:

$\sqrt{\Delta}=\sqrt{1166340}=\sqrt{4*291585}=\sqrt{4}*\sqrt{291585}=2\sqrt{291585}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1080)-2\sqrt{291585}}{2*3}=\frac{1080-2\sqrt{291585}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1080)+2\sqrt{291585}}{2*3}=\frac{1080+2\sqrt{291585}}{6}
$