-8a(a+3)=-5a-39

Solution for -8a(a+3)=-5a-39 equation:

-8a(a+3)=-5a-39

We move all terms to the left:

-8a(a+3)-(-5a-39)=0

We multiply parentheses

-8a^2-24a-(-5a-39)=0

We get rid of parentheses

-8a^2-24a+5a+39=0

We add all the numbers together, and all the variables

-8a^2-19a+39=0

a = -8; b = -19; c = +39;
Δ = b2-4ac
Δ = -192-4·(-8)·39
Δ = 1609
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{-(-19)-\sqrt{1609}}{2*-8}=\frac{19-\sqrt{1609}}{-16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{1609}}{2*-8}=\frac{19+\sqrt{1609}}{-16}
$