10=3p^2-5p-8

Solution for 10=3p^2-5p-8 equation:

10=3p^2-5p-8

We move all terms to the left:

10-(3p^2-5p-8)=0

We get rid of parentheses

-3p^2+5p+8+10=0

We add all the numbers together, and all the variables

-3p^2+5p+18=0

a = -3; b = 5; c = +18;
Δ = b2-4ac
Δ = 52-4·(-3)·18
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{241}}{2*-3}=\frac{-5-\sqrt{241}}{-6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{241}}{2*-3}=\frac{-5+\sqrt{241}}{-6}
$