7^2x-5=1/343

Solution for 7^2x-5=1/343 equation:

7^2x-5=1/343

We move all terms to the left:

7^2x-5-(1/343)=0

We add all the numbers together, and all the variables

7^2x-5-(+1/343)=0

We get rid of parentheses

7^2x-5-1/343=0

We multiply all the terms by the denominator


7^2x*343-1-5*343=0

We add all the numbers together, and all the variables

7^2x*343-1716=0

Wy multiply elements

2401x^2-1716=0

a = 2401; b = 0; c = -1716;
Δ = b2-4ac
Δ = 02-4·2401·(-1716)
Δ = 16480464
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:

$\sqrt{\Delta}=\sqrt{16480464}=\sqrt{38416*429}=\sqrt{38416}*\sqrt{429}=196\sqrt{429}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-196\sqrt{429}}{2*2401}=\frac{0-196\sqrt{429}}{4802}
=-\frac{196\sqrt{429}}{4802}
=-\frac{2\sqrt{429}}{49}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+196\sqrt{429}}{2*2401}=\frac{0+196\sqrt{429}}{4802}
=\frac{196\sqrt{429}}{4802}
=\frac{2\sqrt{429}}{49}
$