9p^2+30p+25=48

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

9p^2+30p+25=48

We move all terms to the left:

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

We add all the numbers together, and all the variables

9p^2+30p-23=0

a = 9; b = 30; c = -23;
Δ = b2-4ac
Δ = 302-4·9·(-23)
Δ = 1728
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:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-24\sqrt{3}}{2*9}=\frac{-30-24\sqrt{3}}{18}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+24\sqrt{3}}{2*9}=\frac{-30+24\sqrt{3}}{18}
$