SOLUTION: Hello, I need an explanation on this problem: 3p^2 + 4p = 5 The answer is P=2ħsqrt(19)/3 For whatever reason, after using the quadratic formula, I get P=-2ħ sqrt(19)/3 As

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Question 819255: Hello, I need an explanation on this problem: 3p^2 + 4p = 5
The answer is P=2ħsqrt(19)/3
For whatever reason, after using the quadratic formula, I get P=-2ħ sqrt(19)/3
As we know, the quadratic formula requires us to change the "4" in the problem to a "-4" [p=-4pħ sqrt4^2-4(3)(-5)/2(3)].
HOW is the "2" a positive number? Please help
Found 2 solutions by solver91311, TimothyLamb:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!
Presuming your answer is

then your answer is correct.

I suspect the book answer is a misprint UNLESS the problem was actually

 or perhaps even 

in which case  is indeed correct.

Answer by TimothyLamb(4379)   (Show Source): You can put this solution on YOUR website!
3p^2 + 4p = 5
3p^2 + 4p - 5 = 0
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the above quadratic equation is in standard form, with a=3, b=4, and c=-5
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to solve the quadratic equation by using the quadratic formula, plug this:
3 4 -5
into this: https://sooeet.com/math/quadratic-equation-solver.php
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the two real roots of the quadratic are:
p = 0.786299648
p = ( -4 + sqrt(4^2 - 4(3)(-5)) ) / 2(3)
p = ( -4 + sqrt(16 - (-60)) ) / 2(3)
p = ( -4 + sqrt(76) ) / 6
p = ( -4 + sqrt(4*19) ) / 6
p = ( -4 + (2)sqrt(19) ) / 6
p = ( -2 + sqrt(19) ) / 3
---
p = -2.11963298
p = ( -4 - sqrt(4^2 - 4(3)(-5)) ) / 2(3)
p = ( -4 - sqrt(16 - (-60)) ) / 2(3)
p = ( -4 - sqrt(76) ) / 6
p = ( -4 - sqrt(4*19) ) / 6
p = ( -4 - (2)sqrt(19) ) / 6
p = ( -2 - sqrt(19) ) / 3
---
Solve and graph linear equations:
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Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
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