3p^2+56=-31p

Solution for 3p^2+56=-31p equation:

3p^2+56=-31p

We move all terms to the left:

3p^2+56-(-31p)=0

We get rid of parentheses

3p^2+31p+56=0

a = 3; b = 31; c = +56;
Δ = b2-4ac
Δ = 312-4·3·56
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-17}{2*3}=\frac{-48}{6}
=-8
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+17}{2*3}=\frac{-14}{6}
=-2+1/3
$