(1/2)2x=162

Solution for (1/2)2x=162 equation:

(1/2)2x=162

We move all terms to the left:

(1/2)2x-(162)=0


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)2x-162=0

We multiply parentheses

2x^2-162=0

a = 2; b = 0; c = -162;
Δ = b2-4ac
Δ = 02-4·2·(-162)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36}{2*2}=\frac{-36}{4}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36}{2*2}=\frac{36}{4}
=9
$