1=6p^2-p

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

1=6p^2-p

We move all terms to the left:

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

We get rid of parentheses

-6p^2+p+1=0

a = -6; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-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{-(1)-5}{2*-6}=\frac{-6}{-12}
=1/2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5}{2*-6}=\frac{4}{-12}
=-1/3
$