10p^2-54p-7=0

Solution for 10p^2-54p-7=0 equation:

10p^2-54p-7=0

a = 10; b = -54; c = -7;
Δ = b2-4ac
Δ = -542-4·10·(-7)
Δ = 3196
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:

$\sqrt{\Delta}=\sqrt{3196}=\sqrt{4*799}=\sqrt{4}*\sqrt{799}=2\sqrt{799}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{799}}{2*10}=\frac{54-2\sqrt{799}}{20}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{799}}{2*10}=\frac{54+2\sqrt{799}}{20}
$