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5-p=4p^2
We move all terms to the left:
5-p-(4p^2)=0
determiningTheFunctionDomain -4p^2-p+5=0
We add all the numbers together, and all the variables
-4p^2-1p+5=0
a = -4; b = -1; c = +5;
Δ = b2-4ac
Δ = -12-4·(-4)·5
Δ = 81
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{81}=9$$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*-4}=\frac{-8}{-8} =1 $$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*-4}=\frac{10}{-8} =-1+1/4 $
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