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

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

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

We move all terms to the left:

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

We multiply parentheses

15b^2+30b-(2b-9)=0

We get rid of parentheses

15b^2+30b-2b+9=0

We add all the numbers together, and all the variables

15b^2+28b+9=0

a = 15; b = 28; c = +9;
Δ = b2-4ac
Δ = 282-4·15·9
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{61}}{2*15}=\frac{-28-2\sqrt{61}}{30}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{61}}{2*15}=\frac{-28+2\sqrt{61}}{30}
$