21x^2-3=0

Solution for 21x^2-3=0 equation:

21x^2-3=0

a = 21; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·21·(-3)
Δ = 252
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{7}}{2*21}=\frac{0-6\sqrt{7}}{42}
=-\frac{6\sqrt{7}}{42}
=-\frac{\sqrt{7}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{7}}{2*21}=\frac{0+6\sqrt{7}}{42}
=\frac{6\sqrt{7}}{42}
=\frac{\sqrt{7}}{7}
$