2x^2/2^x=64

Solution for 2x^2/2^x=64 equation:

2x^2/2^x=64

We move all terms to the left:

2x^2/2^x-(64)=0


Domain of the equation: 2^x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


2x^2-64*2^x=0

Wy multiply elements

2x^2-128x=0

a = 2; b = -128; c = 0;
Δ = b2-4ac
Δ = -1282-4·2·0
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{-(-128)-128}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+128}{2*2}=\frac{256}{4}
=64
$