3p^2+6p=78

Solution for 3p^2+6p=78 equation:

3p^2+6p=78

We move all terms to the left:

3p^2+6p-(78)=0

a = 3; b = 6; c = -78;
Δ = b2-4ac
Δ = 62-4·3·(-78)
Δ = 972
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:

$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-18\sqrt{3}}{2*3}=\frac{-6-18\sqrt{3}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+18\sqrt{3}}{2*3}=\frac{-6+18\sqrt{3}}{6}
$