7p2-2=54p

Solution for 7p2-2=54p equation:

7p^2-2=54p

We move all terms to the left:

7p^2-2-(54p)=0

a = 7; b = -54; c = -2;
Δ = b2-4ac
Δ = -542-4·7·(-2)
Δ = 2972
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:

$\sqrt{\Delta}=\sqrt{2972}=\sqrt{4*743}=\sqrt{4}*\sqrt{743}=2\sqrt{743}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{743}}{2*7}=\frac{54-2\sqrt{743}}{14}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{743}}{2*7}=\frac{54+2\sqrt{743}}{14}
$