7^2x=1/343

Solution for 7^2x=1/343 equation:

7^2x=1/343

We move all terms to the left:

7^2x-(1/343)=0

We add all the numbers together, and all the variables

7^2x-(+1/343)=0

We get rid of parentheses

7^2x-1/343=0

We multiply all the terms by the denominator


7^2x*343-1=0

Wy multiply elements

2401x^2-1=0

a = 2401; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·2401·(-1)
Δ = 9604
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9604}=98$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-98}{2*2401}=\frac{-98}{4802}
=-1/49
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+98}{2*2401}=\frac{98}{4802}
=1/49
$