a(2a+3)=39

Solution for a(2a+3)=39 equation:

a(2a+3)=39

We move all terms to the left:

a(2a+3)-(39)=0

We multiply parentheses

2a^2+3a-39=0

a = 2; b = 3; c = -39;
Δ = b2-4ac
Δ = 32-4·2·(-39)
Δ = 321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{321}}{2*2}=\frac{-3-\sqrt{321}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{321}}{2*2}=\frac{-3+\sqrt{321}}{4}
$