4p^2-12p-120=-8

Solution for 4p^2-12p-120=-8 equation:

4p^2-12p-120=-8

We move all terms to the left:

4p^2-12p-120-(-8)=0

We add all the numbers together, and all the variables

4p^2-12p-112=0

a = 4; b = -12; c = -112;
Δ = b2-4ac
Δ = -122-4·4·(-112)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-44}{2*4}=\frac{-32}{8}
=-4
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+44}{2*4}=\frac{56}{8}
=7
$