3p^2=-14p-6

Solution for 3p^2=-14p-6 equation:

3p^2=-14p-6

We move all terms to the left:

3p^2-(-14p-6)=0

We get rid of parentheses

3p^2+14p+6=0

a = 3; b = 14; c = +6;
Δ = b2-4ac
Δ = 142-4·3·6
Δ = 124
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{31}}{2*3}=\frac{-14-2\sqrt{31}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{31}}{2*3}=\frac{-14+2\sqrt{31}}{6}
$