2^x^2*4^x=256

Solution for 2^x^2*4^x=256 equation:

2^x^2*4^x=256

We move all terms to the left:

2^x^2*4^x-(256)=0

Wy multiply elements

8x^2-256=0

a = 8; b = 0; c = -256;
Δ = b2-4ac
Δ = 02-4·8·(-256)
Δ = 8192
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:

$\sqrt{\Delta}=\sqrt{8192}=\sqrt{4096*2}=\sqrt{4096}*\sqrt{2}=64\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{2}}{2*8}=\frac{0-64\sqrt{2}}{16}
=-\frac{64\sqrt{2}}{16}
=-4\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{2}}{2*8}=\frac{0+64\sqrt{2}}{16}
=\frac{64\sqrt{2}}{16}
=4\sqrt{2}
$