4^x*3^x=91

Solution for 4^x*3^x=91 equation:

4^x*3^x=91

We move all terms to the left:

4^x*3^x-(91)=0

Wy multiply elements

12x^2-91=0

a = 12; b = 0; c = -91;
Δ = b2-4ac
Δ = 02-4·12·(-91)
Δ = 4368
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:

$\sqrt{\Delta}=\sqrt{4368}=\sqrt{16*273}=\sqrt{16}*\sqrt{273}=4\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{273}}{2*12}=\frac{0-4\sqrt{273}}{24}
=-\frac{4\sqrt{273}}{24}
=-\frac{\sqrt{273}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{273}}{2*12}=\frac{0+4\sqrt{273}}{24}
=\frac{4\sqrt{273}}{24}
=\frac{\sqrt{273}}{6}
$