8(3a+6)=9(2a-4)a=

Solution for 8(3a+6)=9(2a-4)a= equation:

8(3a+6)=9(2a-4)a=

We move all terms to the left:

8(3a+6)-(9(2a-4)a)=0

We multiply parentheses

24a-(9(2a-4)a)+48=0


We calculate terms in parentheses: -(9(2a-4)a), so:

9(2a-4)a

We multiply parentheses

18a^2-36a

Back to the equation:

-(18a^2-36a)


We get rid of parentheses

-18a^2+24a+36a+48=0

We add all the numbers together, and all the variables

-18a^2+60a+48=0

a = -18; b = 60; c = +48;
Δ = b2-4ac
Δ = 602-4·(-18)·48
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-84}{2*-18}=\frac{-144}{-36}
=+4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+84}{2*-18}=\frac{24}{-36}
=-2/3
$