1.5(b+2)26b-9=15

Solution for 1.5(b+2)26b-9=15 equation:

1.5(b+2)26b-9=15

We move all terms to the left:

1.5(b+2)26b-9-(15)=0

We add all the numbers together, and all the variables

1.5(b+2)26b-24=0

We multiply parentheses

39b^2+78b-24=0

a = 39; b = 78; c = -24;
Δ = b2-4ac
Δ = 782-4·39·(-24)
Δ = 9828
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:

$\sqrt{\Delta}=\sqrt{9828}=\sqrt{36*273}=\sqrt{36}*\sqrt{273}=6\sqrt{273}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-6\sqrt{273}}{2*39}=\frac{-78-6\sqrt{273}}{78}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+6\sqrt{273}}{2*39}=\frac{-78+6\sqrt{273}}{78}
$