6p^2+5p=-1

Solution for 6p^2+5p=-1 equation:

6p^2+5p=-1

We move all terms to the left:

6p^2+5p-(-1)=0

We add all the numbers together, and all the variables

6p^2+5p+1=0

a = 6; b = 5; c = +1;
Δ = b2-4ac
Δ = 52-4·6·1
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-1}{2*6}=\frac{-6}{12}
=-1/2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+1}{2*6}=\frac{-4}{12}
=-1/3
$