3p^2=-16p-7

Solution for 3p^2=-16p-7 equation:

3p^2=-16p-7

We move all terms to the left:

3p^2-(-16p-7)=0

We get rid of parentheses

3p^2+16p+7=0

a = 3; b = 16; c = +7;
Δ = b2-4ac
Δ = 162-4·3·7
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{43}}{2*3}=\frac{-16-2\sqrt{43}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{43}}{2*3}=\frac{-16+2\sqrt{43}}{6}
$