10p(-6p+12)=1

Solution for 10p(-6p+12)=1 equation:

10p(-6p+12)=1

We move all terms to the left:

10p(-6p+12)-(1)=0

We multiply parentheses

-60p^2+120p-1=0

a = -60; b = 120; c = -1;
Δ = b2-4ac
Δ = 1202-4·(-60)·(-1)
Δ = 14160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14160}=\sqrt{16*885}=\sqrt{16}*\sqrt{885}=4\sqrt{885}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-4\sqrt{885}}{2*-60}=\frac{-120-4\sqrt{885}}{-120}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+4\sqrt{885}}{2*-60}=\frac{-120+4\sqrt{885}}{-120}
$