7p^2+3=54p

Solution for 7p^2+3=54p equation:

7p^2+3=54p

We move all terms to the left:

7p^2+3-(54p)=0

a = 7; b = -54; c = +3;
Δ = b2-4ac
Δ = -542-4·7·3
Δ = 2832
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:

$\sqrt{\Delta}=\sqrt{2832}=\sqrt{16*177}=\sqrt{16}*\sqrt{177}=4\sqrt{177}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-4\sqrt{177}}{2*7}=\frac{54-4\sqrt{177}}{14}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+4\sqrt{177}}{2*7}=\frac{54+4\sqrt{177}}{14}
$