P=16x^2-15

Solution for P=16x^2-15 equation:

=16P^2-15

We move all terms to the left:

-(16P^2-15)=0

We get rid of parentheses

-16P^2+15=0

a = -16; b = 0; c = +15;
Δ = b2-4ac
Δ = 02-4·(-16)·15
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{15}}{2*-16}=\frac{0-8\sqrt{15}}{-32}
=-\frac{8\sqrt{15}}{-32}
=-\frac{\sqrt{15}}{-4}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*-16}=\frac{0+8\sqrt{15}}{-32}
=\frac{8\sqrt{15}}{-32}
=\frac{\sqrt{15}}{-4}
$