4x^2/2^x=16

Solution for 4x^2/2^x=16 equation:

4x^2/2^x=16

We move all terms to the left:

4x^2/2^x-(16)=0


Domain of the equation: 2^x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


4x^2-16*2^x=0

Wy multiply elements

4x^2-32x=0

a = 4; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·4·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*4}=\frac{64}{8}
=8
$