2a(3a+9)-15=57

Solution for 2a(3a+9)-15=57 equation:

2a(3a+9)-15=57

We move all terms to the left:

2a(3a+9)-15-(57)=0

We add all the numbers together, and all the variables

2a(3a+9)-72=0

We multiply parentheses

6a^2+18a-72=0

a = 6; b = 18; c = -72;
Δ = b2-4ac
Δ = 182-4·6·(-72)
Δ = 2052
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2052}=\sqrt{36*57}=\sqrt{36}*\sqrt{57}=6\sqrt{57}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{57}}{2*6}=\frac{-18-6\sqrt{57}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{57}}{2*6}=\frac{-18+6\sqrt{57}}{12}
$