1-3m^2=-21

Solution for 1-3m^2=-21 equation:

1-3m^2=-21

We move all terms to the left:

1-3m^2-(-21)=0

We add all the numbers together, and all the variables

-3m^2+22=0

a = -3; b = 0; c = +22;
Δ = b2-4ac
Δ = 02-4·(-3)·22
Δ = 264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{66}}{2*-3}=\frac{0-2\sqrt{66}}{-6}
=-\frac{2\sqrt{66}}{-6}
=-\frac{\sqrt{66}}{-3}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{66}}{2*-3}=\frac{0+2\sqrt{66}}{-6}
=\frac{2\sqrt{66}}{-6}
=\frac{\sqrt{66}}{-3}
$