3p^2-17p=-10

Solution for 3p^2-17p=-10 equation:

3p^2-17p=-10

We move all terms to the left:

3p^2-17p-(-10)=0

We add all the numbers together, and all the variables

3p^2-17p+10=0

a = 3; b = -17; c = +10;
Δ = b2-4ac
Δ = -172-4·3·10
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-13}{2*3}=\frac{4}{6}
=2/3
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+13}{2*3}=\frac{30}{6}
=5
$