17p+5p^2=-6

Solution for 17p+5p^2=-6 equation:

17p+5p^2=-6

We move all terms to the left:

17p+5p^2-(-6)=0

We add all the numbers together, and all the variables

5p^2+17p+6=0

a = 5; b = 17; c = +6;
Δ = b2-4ac
Δ = 172-4·5·6
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*5}=\frac{-30}{10}
=-3
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+13}{2*5}=\frac{-4}{10}
=-2/5
$