3a^2=250

Solution for 3a^2=250 equation:

3a^2=250

We move all terms to the left:

3a^2-(250)=0

a = 3; b = 0; c = -250;
Δ = b2-4ac
Δ = 02-4·3·(-250)
Δ = 3000
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:

$\sqrt{\Delta}=\sqrt{3000}=\sqrt{100*30}=\sqrt{100}*\sqrt{30}=10\sqrt{30}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{30}}{2*3}=\frac{0-10\sqrt{30}}{6}
=-\frac{10\sqrt{30}}{6}
=-\frac{5\sqrt{30}}{3}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{30}}{2*3}=\frac{0+10\sqrt{30}}{6}
=\frac{10\sqrt{30}}{6}
=\frac{5\sqrt{30}}{3}
$