25p^2+30p+9=50

Solution for 25p^2+30p+9=50 equation:

25p^2+30p+9=50

We move all terms to the left:

25p^2+30p+9-(50)=0

We add all the numbers together, and all the variables

25p^2+30p-41=0

a = 25; b = 30; c = -41;
Δ = b2-4ac
Δ = 302-4·25·(-41)
Δ = 5000
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:

$\sqrt{\Delta}=\sqrt{5000}=\sqrt{2500*2}=\sqrt{2500}*\sqrt{2}=50\sqrt{2}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-50\sqrt{2}}{2*25}=\frac{-30-50\sqrt{2}}{50}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+50\sqrt{2}}{2*25}=\frac{-30+50\sqrt{2}}{50}
$