8(3)=9a(2)

Solution for 8(3)=9a(2) equation:

8(3)=9a(2)

We move all terms to the left:

8(3)-(9a(2))=0

determiningTheFunctionDomain
-9a2+83=0

We add all the numbers together, and all the variables

-9a^2+83=0

a = -9; b = 0; c = +83;
Δ = b2-4ac
Δ = 02-4·(-9)·83
Δ = 2988
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:

$\sqrt{\Delta}=\sqrt{2988}=\sqrt{36*83}=\sqrt{36}*\sqrt{83}=6\sqrt{83}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{83}}{2*-9}=\frac{0-6\sqrt{83}}{-18}
=-\frac{6\sqrt{83}}{-18}
=-\frac{\sqrt{83}}{-3}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{83}}{2*-9}=\frac{0+6\sqrt{83}}{-18}
=\frac{6\sqrt{83}}{-18}
=\frac{\sqrt{83}}{-3}
$