1/49=7^2x

Solution for 1/49=7^2x equation:

1/49=7^2x

We move all terms to the left:

1/49-(7^2x)=0

We multiply all the terms by the denominator


-7^2x*49+1=0

Wy multiply elements

-343x^2+1=0

a = -343; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-343)·1
Δ = 1372
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:

$\sqrt{\Delta}=\sqrt{1372}=\sqrt{196*7}=\sqrt{196}*\sqrt{7}=14\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{7}}{2*-343}=\frac{0-14\sqrt{7}}{-686}
=-\frac{14\sqrt{7}}{-686}
=-\frac{\sqrt{7}}{-49}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{7}}{2*-343}=\frac{0+14\sqrt{7}}{-686}
=\frac{14\sqrt{7}}{-686}
=\frac{\sqrt{7}}{-49}
$