14=8x(2^-x)-2^-x

Solution for 14=8x(2^-x)-2^-x equation:

14=8x(2^-x)-2^-x

We move all terms to the left:

14-(8x(2^-x)-2^-x)=0


We calculate terms in parentheses: -(8x(2^-x)-2^-x), so:

8x(2^-x)-2^-x

determiningTheFunctionDomain
8x(2^-x)-x-2^

We add all the numbers together, and all the variables

-1x+8x(2^-x)

We multiply parentheses

16x^2-8x^2-1x

We add all the numbers together, and all the variables

8x^2-1x

Back to the equation:

-(8x^2-1x)


We get rid of parentheses

-8x^2+1x+14=0

We add all the numbers together, and all the variables

-8x^2+x+14=0

a = -8; b = 1; c = +14;
Δ = b2-4ac
Δ = 12-4·(-8)·14
Δ = 449
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{-(1)-\sqrt{449}}{2*-8}=\frac{-1-\sqrt{449}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{449}}{2*-8}=\frac{-1+\sqrt{449}}{-16}
$