9/46=p^2

Solution for 9/46=p^2 equation:

9/46=p^2

We move all terms to the left:

9/46-(p^2)=0

We add all the numbers together, and all the variables

-1p^2+9/46=0

We multiply all the terms by the denominator


-1p^2*46+9=0

Wy multiply elements

-46p^2+9=0

a = -46; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-46)·9
Δ = 1656
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:

$\sqrt{\Delta}=\sqrt{1656}=\sqrt{36*46}=\sqrt{36}*\sqrt{46}=6\sqrt{46}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{46}}{2*-46}=\frac{0-6\sqrt{46}}{-92}
=-\frac{6\sqrt{46}}{-92}
=-\frac{3\sqrt{46}}{-46}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{46}}{2*-46}=\frac{0+6\sqrt{46}}{-92}
=\frac{6\sqrt{46}}{-92}
=\frac{3\sqrt{46}}{-46}
$