4/9p^2-25=9

Solution for 4/9p^2-25=9 equation:

4/9p^2-25=9

We move all terms to the left:

4/9p^2-25-(9)=0


Domain of the equation: 9p^2!=0

p^2!=0/9

p^2!=√0

p!=0

p∈R


We add all the numbers together, and all the variables

4/9p^2-34=0

We multiply all the terms by the denominator


-34*9p^2+4=0

Wy multiply elements

-306p^2+4=0

a = -306; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-306)·4
Δ = 4896
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:

$\sqrt{\Delta}=\sqrt{4896}=\sqrt{144*34}=\sqrt{144}*\sqrt{34}=12\sqrt{34}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{34}}{2*-306}=\frac{0-12\sqrt{34}}{-612}
=-\frac{12\sqrt{34}}{-612}
=-\frac{\sqrt{34}}{-51}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{34}}{2*-306}=\frac{0+12\sqrt{34}}{-612}
=\frac{12\sqrt{34}}{-612}
=\frac{\sqrt{34}}{-51}
$