8^1*2^x=32^1/2

Solution for 8^1*2^x=32^1/2 equation:

8^1*2^x=32^1/2

We move all terms to the left:

8^1*2^x-(32^1/2)=0

Wy multiply elements

16x^2-(32^1/2)=0

We get rid of parentheses

16x^2-32^1/2=0

We multiply all the terms by the denominator


16x^2*2-32^1=0

We add all the numbers together, and all the variables

16x^2*2-32=0

Wy multiply elements

32x^2-32=0

a = 32; b = 0; c = -32;
Δ = b2-4ac
Δ = 02-4·32·(-32)
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64}{2*32}=\frac{-64}{64}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64}{2*32}=\frac{64}{64}
=1
$