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(P)=-15P^2+750P-6000
We move all terms to the left:
(P)-(-15P^2+750P-6000)=0
We get rid of parentheses
15P^2-750P+P+6000=0
We add all the numbers together, and all the variables
15P^2-749P+6000=0
a = 15; b = -749; c = +6000;
Δ = b2-4ac
Δ = -7492-4·15·6000
Δ = 201001
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}$$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-749)-\sqrt{201001}}{2*15}=\frac{749-\sqrt{201001}}{30} $$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-749)+\sqrt{201001}}{2*15}=\frac{749+\sqrt{201001}}{30} $
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