(54p^2)-1368p+90=0

Solution for (54p^2)-1368p+90=0 equation:

(54p^2)-1368p+90=0

a = 54; b = -1368; c = +90;
Δ = b2-4ac
Δ = -13682-4·54·90
Δ = 1851984
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:

$\sqrt{\Delta}=\sqrt{1851984}=\sqrt{1296*1429}=\sqrt{1296}*\sqrt{1429}=36\sqrt{1429}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1368)-36\sqrt{1429}}{2*54}=\frac{1368-36\sqrt{1429}}{108}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1368)+36\sqrt{1429}}{2*54}=\frac{1368+36\sqrt{1429}}{108}
$