12p2=-8-28p

Solution for 12p2=-8-28p equation:

12p^2=-8-28p

We move all terms to the left:

12p^2-(-8-28p)=0

We add all the numbers together, and all the variables

12p^2-(-28p-8)=0

We get rid of parentheses

12p^2+28p+8=0

a = 12; b = 28; c = +8;
Δ = b2-4ac
Δ = 282-4·12·8
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-20}{2*12}=\frac{-48}{24}
=-2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+20}{2*12}=\frac{-8}{24}
=-1/3
$