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p*5p=4.5
We move all terms to the left:
p*5p-(4.5)=0
We add all the numbers together, and all the variables
p*5p-4.5=0
Wy multiply elements
5p^2-4.5=0
a = 5; b = 0; c = -4.5;
Δ = b2-4ac
Δ = 02-4·5·(-4.5)
Δ = 90
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}$$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{90}=\sqrt{9*10}=\sqrt{9}*\sqrt{10}=3\sqrt{10}$$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{10}}{2*5}=\frac{0-3\sqrt{10}}{10} =-\frac{3\sqrt{10}}{10} $$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{10}}{2*5}=\frac{0+3\sqrt{10}}{10} =\frac{3\sqrt{10}}{10} $
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