2^x*3^x=144

Solution for 2^x*3^x=144 equation:

2^x*3^x=144

We move all terms to the left:

2^x*3^x-(144)=0

Wy multiply elements

6x^2-144=0

a = 6; b = 0; c = -144;
Δ = b2-4ac
Δ = 02-4·6·(-144)
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*6}=\frac{0-24\sqrt{6}}{12}
=-\frac{24\sqrt{6}}{12}
=-2\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{6}}{2*6}=\frac{0+24\sqrt{6}}{12}
=\frac{24\sqrt{6}}{12}
=2\sqrt{6}
$