6.9^x-13.6^x+6.4^1/x=0

Solution for 6.9^x-13.6^x+6.4^1/x=0 equation:

6.9^x-13.6^x+6.4^1/x=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


(6.9^x)*x-(13.6^x)*x+6.4^1=0

We add all the numbers together, and all the variables

(6.9^x)*x-(13.6^x)*x+6.4=0

We multiply parentheses

6x^2-13x^2+6.4=0

We add all the numbers together, and all the variables

-7x^2+6.4=0

a = -7; b = 0; c = +6.4;
Δ = b2-4ac
Δ = 02-4·(-7)·6.4
Δ = 179.2
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-\sqrt{179.2}}{2*-7}=\frac{0-\sqrt{179.2}}{-14}
=-\frac{\sqrt{}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+\sqrt{179.2}}{2*-7}=\frac{0+\sqrt{179.2}}{-14}
=\frac{\sqrt{}}{-14}
$