x-1/3x=360

Solution for x-1/3x=360 equation:

x-1/3x=360

We move all terms to the left:

x-1/3x-(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=0

Wy multiply elements

3x^2-1080x-1=0

a = 3; b = -1080; c = -1;
Δ = b2-4ac
Δ = -10802-4·3·(-1)
Δ = 1166412
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:

$\sqrt{\Delta}=\sqrt{1166412}=\sqrt{4*291603}=\sqrt{4}*\sqrt{291603}=2\sqrt{291603}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1080)-2\sqrt{291603}}{2*3}=\frac{1080-2\sqrt{291603}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1080)+2\sqrt{291603}}{2*3}=\frac{1080+2\sqrt{291603}}{6}
$