3p^2-20p-34=10

Solution for 3p^2-20p-34=10 equation:

3p^2-20p-34=10

We move all terms to the left:

3p^2-20p-34-(10)=0

We add all the numbers together, and all the variables

3p^2-20p-44=0

a = 3; b = -20; c = -44;
Δ = b2-4ac
Δ = -202-4·3·(-44)
Δ = 928
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:

$\sqrt{\Delta}=\sqrt{928}=\sqrt{16*58}=\sqrt{16}*\sqrt{58}=4\sqrt{58}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{58}}{2*3}=\frac{20-4\sqrt{58}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{58}}{2*3}=\frac{20+4\sqrt{58}}{6}
$