6a^2=10

Solution for 6a^2=10 equation:

6a^2=10

We move all terms to the left:

6a^2-(10)=0

a = 6; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·6·(-10)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*6}=\frac{0-4\sqrt{15}}{12}
=-\frac{4\sqrt{15}}{12}
=-\frac{\sqrt{15}}{3}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*6}=\frac{0+4\sqrt{15}}{12}
=\frac{4\sqrt{15}}{12}
=\frac{\sqrt{15}}{3}
$