x-2/3x=180

Solution for x-2/3x=180 equation:

x-2/3x=180

We move all terms to the left:

x-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-2=0

Wy multiply elements

3x^2-540x-2=0

a = 3; b = -540; c = -2;
Δ = b2-4ac
Δ = -5402-4·3·(-2)
Δ = 291624
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:

$\sqrt{\Delta}=\sqrt{291624}=\sqrt{4*72906}=\sqrt{4}*\sqrt{72906}=2\sqrt{72906}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-2\sqrt{72906}}{2*3}=\frac{540-2\sqrt{72906}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+2\sqrt{72906}}{2*3}=\frac{540+2\sqrt{72906}}{6}
$