4p^2=-5-12p

Solution for 4p^2=-5-12p equation:

4p^2=-5-12p

We move all terms to the left:

4p^2-(-5-12p)=0

We add all the numbers together, and all the variables

4p^2-(-12p-5)=0

We get rid of parentheses

4p^2+12p+5=0

a = 4; b = 12; c = +5;
Δ = b2-4ac
Δ = 122-4·4·5
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8}{2*4}=\frac{-20}{8}
=-2+1/2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8}{2*4}=\frac{-4}{8}
=-1/2
$