12p2-8=-3p

Solution for 12p2-8=-3p equation:

12p^2-8=-3p

We move all terms to the left:

12p^2-8-(-3p)=0

We get rid of parentheses

12p^2+3p-8=0

a = 12; b = 3; c = -8;
Δ = b2-4ac
Δ = 32-4·12·(-8)
Δ = 393
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{393}}{2*12}=\frac{-3-\sqrt{393}}{24}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{393}}{2*12}=\frac{-3+\sqrt{393}}{24}
$