7p+6p^2=-1

Solution for 7p+6p^2=-1 equation:

7p+6p^2=-1

We move all terms to the left:

7p+6p^2-(-1)=0

We add all the numbers together, and all the variables

6p^2+7p+1=0

a = 6; b = 7; c = +1;
Δ = b2-4ac
Δ = 72-4·6·1
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-5}{2*6}=\frac{-12}{12}
=-1
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+5}{2*6}=\frac{-2}{12}
=-1/6
$