a*6a=500

Solution for a*6a=500 equation:

a*6a=500

We move all terms to the left:

a*6a-(500)=0

Wy multiply elements

6a^2-500=0

a = 6; b = 0; c = -500;
Δ = b2-4ac
Δ = 02-4·6·(-500)
Δ = 12000
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:

$\sqrt{\Delta}=\sqrt{12000}=\sqrt{400*30}=\sqrt{400}*\sqrt{30}=20\sqrt{30}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{30}}{2*6}=\frac{0-20\sqrt{30}}{12}
=-\frac{20\sqrt{30}}{12}
=-\frac{5\sqrt{30}}{3}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{30}}{2*6}=\frac{0+20\sqrt{30}}{12}
=\frac{20\sqrt{30}}{12}
=\frac{5\sqrt{30}}{3}
$