7^x+343/7^x=56

Solution for 7^x+343/7^x=56 equation:

7^x+343/7^x=56

We move all terms to the left:

7^x+343/7^x-(56)=0


Domain of the equation: 7^x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


7^x*7^x-56*7^x+343=0

Wy multiply elements

49x^2-392x+343=0

a = 49; b = -392; c = +343;
Δ = b2-4ac
Δ = -3922-4·49·343
Δ = 86436
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{86436}=294$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-392)-294}{2*49}=\frac{98}{98}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-392)+294}{2*49}=\frac{686}{98}
=7
$