31p+6p^2=-5

Solution for 31p+6p^2=-5 equation:

31p+6p^2=-5

We move all terms to the left:

31p+6p^2-(-5)=0

We add all the numbers together, and all the variables

6p^2+31p+5=0

a = 6; b = 31; c = +5;
Δ = b2-4ac
Δ = 312-4·6·5
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-29}{2*6}=\frac{-60}{12}
=-5
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+29}{2*6}=\frac{-2}{12}
=-1/6
$