388=1/2b*4b

Solution for 388=1/2b*4b equation:

388=1/2b*4b

We move all terms to the left:

388-(1/2b*4b)=0


Domain of the equation: 2b*4b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

-(+1/2b*4b)+388=0

We get rid of parentheses

-1/2b*4b+388=0

We multiply all the terms by the denominator


388*2b*4b-1=0

Wy multiply elements

3104b^2*4-1=0

Wy multiply elements

12416b^2-1=0

a = 12416; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·12416·(-1)
Δ = 49664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{49664}=\sqrt{256*194}=\sqrt{256}*\sqrt{194}=16\sqrt{194}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{194}}{2*12416}=\frac{0-16\sqrt{194}}{24832}
=-\frac{16\sqrt{194}}{24832}
=-\frac{\sqrt{194}}{1552}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{194}}{2*12416}=\frac{0+16\sqrt{194}}{24832}
=\frac{16\sqrt{194}}{24832}
=\frac{\sqrt{194}}{1552}
$