-12x^2+21=0

Solution for -12x^2+21=0 equation:

-12x^2+21=0

a = -12; b = 0; c = +21;
Δ = b2-4ac
Δ = 02-4·(-12)·21
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{7}}{2*-12}=\frac{0-12\sqrt{7}}{-24}
=-\frac{12\sqrt{7}}{-24}
=-\frac{\sqrt{7}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{7}}{2*-12}=\frac{0+12\sqrt{7}}{-24}
=\frac{12\sqrt{7}}{-24}
=\frac{\sqrt{7}}{-2}
$