25p^2+30p+9=48

Solution for 25p^2+30p+9=48 equation:

25p^2+30p+9=48

We move all terms to the left:

25p^2+30p+9-(48)=0

We add all the numbers together, and all the variables

25p^2+30p-39=0

a = 25; b = 30; c = -39;
Δ = b2-4ac
Δ = 302-4·25·(-39)
Δ = 4800
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:

$\sqrt{\Delta}=\sqrt{4800}=\sqrt{1600*3}=\sqrt{1600}*\sqrt{3}=40\sqrt{3}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-40\sqrt{3}}{2*25}=\frac{-30-40\sqrt{3}}{50}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+40\sqrt{3}}{2*25}=\frac{-30+40\sqrt{3}}{50}
$