a*3a=32000

Solution for a*3a=32000 equation:

a*3a=32000

We move all terms to the left:

a*3a-(32000)=0

Wy multiply elements

3a^2-32000=0

a = 3; b = 0; c = -32000;
Δ = b2-4ac
Δ = 02-4·3·(-32000)
Δ = 384000
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:

$\sqrt{\Delta}=\sqrt{384000}=\sqrt{25600*15}=\sqrt{25600}*\sqrt{15}=160\sqrt{15}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-160\sqrt{15}}{2*3}=\frac{0-160\sqrt{15}}{6}
=-\frac{160\sqrt{15}}{6}
=-\frac{80\sqrt{15}}{3}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+160\sqrt{15}}{2*3}=\frac{0+160\sqrt{15}}{6}
=\frac{160\sqrt{15}}{6}
=\frac{80\sqrt{15}}{3}
$