3^x-(14/3^x)=5

Solution for 3^x-(14/3^x)=5 equation:

3^x-(14/3^x)=5

We move all terms to the left:

3^x-(14/3^x)-(5)=0


Domain of the equation: 3^x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

3^x-14/3^x-5=0

We multiply all the terms by the denominator


3^x*3^x-5*3^x-14=0

Wy multiply elements

9x^2-15x-14=0

a = 9; b = -15; c = -14;
Δ = b2-4ac
Δ = -152-4·9·(-14)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-27}{2*9}=\frac{-12}{18}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+27}{2*9}=\frac{42}{18}
=2+1/3
$