5^x*4^x=60

Solution for 5^x*4^x=60 equation:

5^x*4^x=60

We move all terms to the left:

5^x*4^x-(60)=0

Wy multiply elements

20x^2-60=0

a = 20; b = 0; c = -60;
Δ = b2-4ac
Δ = 02-4·20·(-60)
Δ = 4800
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:

$\sqrt{\Delta}=\sqrt{4800}=\sqrt{1600*3}=\sqrt{1600}*\sqrt{3}=40\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{3}}{2*20}=\frac{0-40\sqrt{3}}{40}
=-\frac{40\sqrt{3}}{40}
=-\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{3}}{2*20}=\frac{0+40\sqrt{3}}{40}
=\frac{40\sqrt{3}}{40}
=\sqrt{3}
$