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4p^2-10p-72=0
a = 4; b = -10; c = -72;
Δ = b2-4ac
Δ = -102-4·4·(-72)
Δ = 1252
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}$$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1252}=\sqrt{4*313}=\sqrt{4}*\sqrt{313}=2\sqrt{313}$$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{313}}{2*4}=\frac{10-2\sqrt{313}}{8} $$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{313}}{2*4}=\frac{10+2\sqrt{313}}{8} $
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