b(b+6)(.5)=36

Solution for b(b+6)(.5)=36 equation:

b(b+6)(.5)=36

We move all terms to the left:

b(b+6)(.5)-(36)=0

We add all the numbers together, and all the variables

b(b+6)(0.5)-36=0

We multiply parentheses ..

b(+0.5b+3)-36=0

We add all the numbers together, and all the variables

b(0.5b+3)-36=0

We multiply parentheses

0b^2+3b-36=0

We add all the numbers together, and all the variables

b^2+3b-36=0

a = 1; b = 3; c = -36;
Δ = b2-4ac
Δ = 32-4·1·(-36)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{17}}{2*1}=\frac{-3-3\sqrt{17}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{17}}{2*1}=\frac{-3+3\sqrt{17}}{2}
$