2/3*x=144

Solution for 2/3*x=144 equation:

2/3*x=144

We move all terms to the left:

2/3*x-(144)=0


Domain of the equation: 3*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-144*3*x+2=0

Wy multiply elements

-432x*x+2=0

Wy multiply elements

-432x^2+2=0

a = -432; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-432)·2
Δ = 3456
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:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{6}}{2*-432}=\frac{0-24\sqrt{6}}{-864}
=-\frac{24\sqrt{6}}{-864}
=-\frac{\sqrt{6}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{6}}{2*-432}=\frac{0+24\sqrt{6}}{-864}
=\frac{24\sqrt{6}}{-864}
=\frac{\sqrt{6}}{-36}
$