2/3x-2x=180

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

2/3x-2x=180

We move all terms to the left:

2/3x-2x-(180)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+2/3x-180=0

We multiply all the terms by the denominator


-2x*3x-180*3x+2=0

Wy multiply elements

-6x^2-540x+2=0

a = -6; b = -540; c = +2;
Δ = b2-4ac
Δ = -5402-4·(-6)·2
Δ = 291648
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:

$\sqrt{\Delta}=\sqrt{291648}=\sqrt{3136*93}=\sqrt{3136}*\sqrt{93}=56\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-56\sqrt{93}}{2*-6}=\frac{540-56\sqrt{93}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+56\sqrt{93}}{2*-6}=\frac{540+56\sqrt{93}}{-12}
$