3a^2-68=0

Solution for 3a^2-68=0 equation:

3a^2-68=0

a = 3; b = 0; c = -68;
Δ = b2-4ac
Δ = 02-4·3·(-68)
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{51}}{2*3}=\frac{0-4\sqrt{51}}{6}
=-\frac{4\sqrt{51}}{6}
=-\frac{2\sqrt{51}}{3}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{51}}{2*3}=\frac{0+4\sqrt{51}}{6}
=\frac{4\sqrt{51}}{6}
=\frac{2\sqrt{51}}{3}
$