56=1/2a2^a=

Solution for 56=1/2a2^a= equation:

56=1/2a^2^a=

We move all terms to the left:

56-(1/2a^2^a)=0


Domain of the equation: 2a^2^a)!=0

a!=0/1

a!=0

a∈R


We get rid of parentheses

-1/2a^2^a+56=0

We multiply all the terms by the denominator


56*2a^2^a-1=0

Wy multiply elements

112a^2-1=0

a = 112; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·112·(-1)
Δ = 448
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{7}}{2*112}=\frac{0-8\sqrt{7}}{224}
=-\frac{8\sqrt{7}}{224}
=-\frac{\sqrt{7}}{28}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{7}}{2*112}=\frac{0+8\sqrt{7}}{224}
=\frac{8\sqrt{7}}{224}
=\frac{\sqrt{7}}{28}
$