3+0.5a(4a+8)=9-2a

Solution for 3+0.5a(4a+8)=9-2a equation:

3+0.5a(4a+8)=9-2a

We move all terms to the left:

3+0.5a(4a+8)-(9-2a)=0

We add all the numbers together, and all the variables

0.5a(4a+8)-(-2a+9)+3=0

We multiply parentheses

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

We get rid of parentheses

0a^2+0a+2a-9+3=0

We add all the numbers together, and all the variables

a^2+3a-6=0

a = 1; b = 3; c = -6;
Δ = b2-4ac
Δ = 32-4·1·(-6)
Δ = 33
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{33}}{2*1}=\frac{-3-\sqrt{33}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{33}}{2*1}=\frac{-3+\sqrt{33}}{2}
$