x*2^x=2048

Solution for x*2^x=2048 equation:

x*2^x=2048

We move all terms to the left:

x*2^x-(2048)=0

Wy multiply elements

2x^2-2048=0

a = 2; b = 0; c = -2048;
Δ = b2-4ac
Δ = 02-4·2·(-2048)
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-128}{2*2}=\frac{-128}{4}
=-32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+128}{2*2}=\frac{128}{4}
=32
$