4^x*0.5^(x+2)=(0.125)^-5

Solution for 4^x*0.5^(x+2)=(0.125)^-5 equation:

4^x*0.5^(x+2)=(0.125)^-5

We move all terms to the left:

4^x*0.5^(x+2)-((0.125)^-5)=0

We add all the numbers together, and all the variables

4^x*0.5^(x+2)-32768=0

Wy multiply elements

0x^2-32768=0

We add all the numbers together, and all the variables

x^2-32768=0

a = 1; b = 0; c = -32768;
Δ = b2-4ac
Δ = 02-4·1·(-32768)
Δ = 131072
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:

$\sqrt{\Delta}=\sqrt{131072}=\sqrt{65536*2}=\sqrt{65536}*\sqrt{2}=256\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-256\sqrt{2}}{2*1}=\frac{0-256\sqrt{2}}{2}
=-\frac{256\sqrt{2}}{2}
=-128\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+256\sqrt{2}}{2*1}=\frac{0+256\sqrt{2}}{2}
=\frac{256\sqrt{2}}{2}
=128\sqrt{2}
$