7/11^x=7(11^x)

Solution for 7/11^x=7(11^x) equation:

7/11^x=7(11^x)

We move all terms to the left:

7/11^x-(7(11^x))=0


Domain of the equation: 11^x!=0

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
7/11^x-711^x=0

We multiply all the terms by the denominator


-711^x*11^x+7=0

Wy multiply elements

-7821x^2+7=0

a = -7821; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-7821)·7
Δ = 218988
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:

$\sqrt{\Delta}=\sqrt{218988}=\sqrt{36*6083}=\sqrt{36}*\sqrt{6083}=6\sqrt{6083}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6083}}{2*-7821}=\frac{0-6\sqrt{6083}}{-15642}
=-\frac{6\sqrt{6083}}{-15642}
=-\frac{\sqrt{6083}}{-2607}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6083}}{2*-7821}=\frac{0+6\sqrt{6083}}{-15642}
=\frac{6\sqrt{6083}}{-15642}
=\frac{\sqrt{6083}}{-2607}
$