8a(a+2)=9

Solution for 8a(a+2)=9 equation:

8a(a+2)=9

We move all terms to the left:

8a(a+2)-(9)=0

We multiply parentheses

8a^2+16a-9=0

a = 8; b = 16; c = -9;
Δ = b2-4ac
Δ = 162-4·8·(-9)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{34}}{2*8}=\frac{-16-4\sqrt{34}}{16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{34}}{2*8}=\frac{-16+4\sqrt{34}}{16}
$