8^x*4^(x^2)-6=4

Solution for 8^x*4^(x^2)-6=4 equation:

8^x*4^(x^2)-6=4

We move all terms to the left:

8^x*4^(x^2)-6-(4)=0

We add all the numbers together, and all the variables

8^x*4^x^2-10=0

Wy multiply elements

32x^2-10=0

a = 32; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·32·(-10)
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{5}}{2*32}=\frac{0-16\sqrt{5}}{64}
=-\frac{16\sqrt{5}}{64}
=-\frac{\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{5}}{2*32}=\frac{0+16\sqrt{5}}{64}
=\frac{16\sqrt{5}}{64}
=\frac{\sqrt{5}}{4}
$