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(P)=7+3P-5P^2
We move all terms to the left:
(P)-(7+3P-5P^2)=0
We get rid of parentheses
5P^2-3P+P-7=0
We add all the numbers together, and all the variables
5P^2-2P-7=0
a = 5; b = -2; c = -7;
Δ = b2-4ac
Δ = -22-4·5·(-7)
Δ = 144
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}$$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{144}=12$$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-12}{2*5}=\frac{-10}{10} =-1 $$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+12}{2*5}=\frac{14}{10} =1+2/5 $
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