64^x=4^(-1/7)

Solution for 64^x=4^(-1/7) equation:

64^x=4^(-1/7)

We move all terms to the left:

64^x-(4^(-1/7))=0

We multiply all the terms by the denominator


64^x*7))-(4^(-1=0

Wy multiply elements

448x^2-1=0

a = 448; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·448·(-1)
Δ = 1792
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:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{7}}{2*448}=\frac{0-16\sqrt{7}}{896}
=-\frac{16\sqrt{7}}{896}
=-\frac{\sqrt{7}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{7}}{2*448}=\frac{0+16\sqrt{7}}{896}
=\frac{16\sqrt{7}}{896}
=\frac{\sqrt{7}}{56}
$