100p+5p^2=10

Solution for 100p+5p^2=10 equation:

100p+5p^2=10

We move all terms to the left:

100p+5p^2-(10)=0

a = 5; b = 100; c = -10;
Δ = b2-4ac
Δ = 1002-4·5·(-10)
Δ = 10200
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:

$\sqrt{\Delta}=\sqrt{10200}=\sqrt{100*102}=\sqrt{100}*\sqrt{102}=10\sqrt{102}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-10\sqrt{102}}{2*5}=\frac{-100-10\sqrt{102}}{10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+10\sqrt{102}}{2*5}=\frac{-100+10\sqrt{102}}{10}
$