1.5(b+2)2b-9b=15

Solution for 1.5(b+2)2b-9b=15 equation:

1.5(b+2)2b-9b=15

We move all terms to the left:

1.5(b+2)2b-9b-(15)=0

We add all the numbers together, and all the variables

-9b+1.5(b+2)2b-15=0

We multiply parentheses

3b^2-9b+6b-15=0

We add all the numbers together, and all the variables

3b^2-3b-15=0

a = 3; b = -3; c = -15;
Δ = b2-4ac
Δ = -32-4·3·(-15)
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{21}}{2*3}=\frac{3-3\sqrt{21}}{6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{21}}{2*3}=\frac{3+3\sqrt{21}}{6}
$