9-1/2p^2=-15

Solution for 9-1/2p^2=-15 equation:

9-1/2p^2=-15

We move all terms to the left:

9-1/2p^2-(-15)=0


Domain of the equation: 2p^2!=0

p^2!=0/2

p^2!=√0

p!=0

p∈R


We add all the numbers together, and all the variables

-1/2p^2+24=0

We multiply all the terms by the denominator


24*2p^2-1=0

Wy multiply elements

48p^2-1=0

a = 48; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·48·(-1)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*48}=\frac{0-8\sqrt{3}}{96}
=-\frac{8\sqrt{3}}{96}
=-\frac{\sqrt{3}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*48}=\frac{0+8\sqrt{3}}{96}
=\frac{8\sqrt{3}}{96}
=\frac{\sqrt{3}}{12}
$