3/2x2^x=24

Solution for 3/2x2^x=24 equation:

3/2x^2^x=24

We move all terms to the left:

3/2x^2^x-(24)=0


Domain of the equation: 2x^2^x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-24*2x^2^x+3=0

Wy multiply elements

-48x^2+3=0

a = -48; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-48)·3
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*-48}=\frac{-24}{-96}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*-48}=\frac{24}{-96}
=-1/4
$