168=1/2(12)b2

Solution for 168=1/2(12)b2 equation:

168=1/2(12)b2

We move all terms to the left:

168-(1/2(12)b2)=0


Domain of the equation: 212b2)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

-(+1/212b2)+168=0

We get rid of parentheses

-1/212b2+168=0

We multiply all the terms by the denominator


168*212b2-1=0

Wy multiply elements

35616b^2-1=0

a = 35616; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·35616·(-1)
Δ = 142464
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:

$\sqrt{\Delta}=\sqrt{142464}=\sqrt{64*2226}=\sqrt{64}*\sqrt{2226}=8\sqrt{2226}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{2226}}{2*35616}=\frac{0-8\sqrt{2226}}{71232}
=-\frac{8\sqrt{2226}}{71232}
=-\frac{\sqrt{2226}}{8904}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{2226}}{2*35616}=\frac{0+8\sqrt{2226}}{71232}
=\frac{8\sqrt{2226}}{71232}
=\frac{\sqrt{2226}}{8904}
$