3a^2=7

Solution for 3a^2=7 equation:

3a^2=7

We move all terms to the left:

3a^2-(7)=0

a = 3; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·3·(-7)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{21}}{2*3}=\frac{0-2\sqrt{21}}{6}
=-\frac{2\sqrt{21}}{6}
=-\frac{\sqrt{21}}{3}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{21}}{2*3}=\frac{0+2\sqrt{21}}{6}
=\frac{2\sqrt{21}}{6}
=\frac{\sqrt{21}}{3}
$