216=1/2*b*6

Solution for 216=1/2*b*6 equation:

216=1/2*b*6

We move all terms to the left:

216-(1/2*b*6)=0


Domain of the equation: 2*b*6)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

-(+1/2*b*6)+216=0

We get rid of parentheses

-1/2*b*6+216=0

We multiply all the terms by the denominator


216*2*b*6-1=0

Wy multiply elements

2592b*b-1=0

Wy multiply elements

2592b^2-1=0

a = 2592; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·2592·(-1)
Δ = 10368
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:

$\sqrt{\Delta}=\sqrt{10368}=\sqrt{5184*2}=\sqrt{5184}*\sqrt{2}=72\sqrt{2}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72\sqrt{2}}{2*2592}=\frac{0-72\sqrt{2}}{5184}
=-\frac{72\sqrt{2}}{5184}
=-\frac{\sqrt{2}}{72}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72\sqrt{2}}{2*2592}=\frac{0+72\sqrt{2}}{5184}
=\frac{72\sqrt{2}}{5184}
=\frac{\sqrt{2}}{72}
$