7p^2-1=-7p

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

7p^2-1=-7p

We move all terms to the left:

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

We get rid of parentheses

7p^2+7p-1=0

a = 7; b = 7; c = -1;
Δ = b2-4ac
Δ = 72-4·7·(-1)
Δ = 77
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{77}}{2*7}=\frac{-7-\sqrt{77}}{14}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{77}}{2*7}=\frac{-7+\sqrt{77}}{14}
$