3p^2+36p=-21

Solution for 3p^2+36p=-21 equation:

3p^2+36p=-21

We move all terms to the left:

3p^2+36p-(-21)=0

We add all the numbers together, and all the variables

3p^2+36p+21=0

a = 3; b = 36; c = +21;
Δ = b2-4ac
Δ = 362-4·3·21
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-6\sqrt{29}}{2*3}=\frac{-36-6\sqrt{29}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+6\sqrt{29}}{2*3}=\frac{-36+6\sqrt{29}}{6}
$