-3p2+5p+5=8p2

Solution for -3p2+5p+5=8p2 equation:

-3p^2+5p+5=8p^2

We move all terms to the left:

-3p^2+5p+5-(8p^2)=0

determiningTheFunctionDomain
-3p^2-8p^2+5p+5=0

We add all the numbers together, and all the variables

-11p^2+5p+5=0

a = -11; b = 5; c = +5;
Δ = b2-4ac
Δ = 52-4·(-11)·5
Δ = 245
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:

$\sqrt{\Delta}=\sqrt{245}=\sqrt{49*5}=\sqrt{49}*\sqrt{5}=7\sqrt{5}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-7\sqrt{5}}{2*-11}=\frac{-5-7\sqrt{5}}{-22}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7\sqrt{5}}{2*-11}=\frac{-5+7\sqrt{5}}{-22}
$