2p^2+7p-8=-12

Solution for 2p^2+7p-8=-12 equation:

2p^2+7p-8=-12

We move all terms to the left:

2p^2+7p-8-(-12)=0

We add all the numbers together, and all the variables

2p^2+7p+4=0

a = 2; b = 7; c = +4;
Δ = b2-4ac
Δ = 72-4·2·4
Δ = 17
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{-(7)-\sqrt{17}}{2*2}=\frac{-7-\sqrt{17}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{17}}{2*2}=\frac{-7+\sqrt{17}}{4}
$