1/2^x+3x+8=0

Solution for 1/2^x+3x+8=0 equation:

1/2^x+3x+8=0


Domain of the equation: 2^x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/2^x+8=0

We multiply all the terms by the denominator


3x*2^x+8*2^x+1=0

Wy multiply elements

6x^2+16x+1=0

a = 6; b = 16; c = +1;
Δ = b2-4ac
Δ = 162-4·6·1
Δ = 232
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:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{58}}{2*6}=\frac{-16-2\sqrt{58}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{58}}{2*6}=\frac{-16+2\sqrt{58}}{12}
$