10p+5p^2=5

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

10p+5p^2=5

We move all terms to the left:

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

a = 5; b = 10; c = -5;
Δ = b2-4ac
Δ = 102-4·5·(-5)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{2}}{2*5}=\frac{-10-10\sqrt{2}}{10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{2}}{2*5}=\frac{-10+10\sqrt{2}}{10}
$