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16-3p=(2)/(5)p+5
We move all terms to the left:
16-3p-((2)/(5)p+5)=0
Domain of the equation: 5p+5)!=0We get rid of parentheses
p∈R
-3p-2/5p-5+16=0
We multiply all the terms by the denominator
-3p*5p-5*5p+16*5p-2=0
Wy multiply elements
-15p^2-25p+80p-2=0
We add all the numbers together, and all the variables
-15p^2+55p-2=0
a = -15; b = 55; c = -2;
Δ = b2-4ac
Δ = 552-4·(-15)·(-2)
Δ = 2905
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{-(55)-\sqrt{2905}}{2*-15}=\frac{-55-\sqrt{2905}}{-30} $$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+\sqrt{2905}}{2*-15}=\frac{-55+\sqrt{2905}}{-30} $
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