a*6a=500000

Solution for a*6a=500000 equation:

a*6a=500000

We move all terms to the left:

a*6a-(500000)=0

Wy multiply elements

6a^2-500000=0

a = 6; b = 0; c = -500000;
Δ = b2-4ac
Δ = 02-4·6·(-500000)
Δ = 12000000
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:

$\sqrt{\Delta}=\sqrt{12000000}=\sqrt{4000000*3}=\sqrt{4000000}*\sqrt{3}=2000\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2000\sqrt{3}}{2*6}=\frac{0-2000\sqrt{3}}{12}
=-\frac{2000\sqrt{3}}{12}
=-\frac{500\sqrt{3}}{3}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2000\sqrt{3}}{2*6}=\frac{0+2000\sqrt{3}}{12}
=\frac{2000\sqrt{3}}{12}
=\frac{500\sqrt{3}}{3}
$