8p^2+22p=-12

Solution for 8p^2+22p=-12 equation:

8p^2+22p=-12

We move all terms to the left:

8p^2+22p-(-12)=0

We add all the numbers together, and all the variables

8p^2+22p+12=0

a = 8; b = 22; c = +12;
Δ = b2-4ac
Δ = 222-4·8·12
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-10}{2*8}=\frac{-32}{16}
=-2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+10}{2*8}=\frac{-12}{16}
=-3/4
$