P=16x^2-12

Solution for P=16x^2-12 equation:

=16P^2-12

We move all terms to the left:

-(16P^2-12)=0

We get rid of parentheses

-16P^2+12=0

a = -16; b = 0; c = +12;
Δ = b2-4ac
Δ = 02-4·(-16)·12
Δ = 768
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{3}}{2*-16}=\frac{0-16\sqrt{3}}{-32}
=-\frac{16\sqrt{3}}{-32}
=-\frac{\sqrt{3}}{-2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{3}}{2*-16}=\frac{0+16\sqrt{3}}{-32}
=\frac{16\sqrt{3}}{-32}
=\frac{\sqrt{3}}{-2}
$