8a(a+2)=5a+16+3a

Solution for 8a(a+2)=5a+16+3a equation:

8a(a+2)=5a+16+3a

We move all terms to the left:

8a(a+2)-(5a+16+3a)=0

We add all the numbers together, and all the variables

8a(a+2)-(8a+16)=0

We multiply parentheses

8a^2+16a-(8a+16)=0

We get rid of parentheses

8a^2+16a-8a-16=0

We add all the numbers together, and all the variables

8a^2+8a-16=0

a = 8; b = 8; c = -16;
Δ = b2-4ac
Δ = 82-4·8·(-16)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-24}{2*8}=\frac{-32}{16}
=-2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+24}{2*8}=\frac{16}{16}
=1
$