# Solve for p 2p^2=6p-20 2p2=6p-20
Subtract 6p from both sides of the equation.
2p2-6p=-20
Move 20 to the left side of the equation by adding it to both sides.
2p2-6p+20=0
Factor 2 out of 2p2-6p+20.
Factor 2 out of 2p2.
2(p2)-6p+20=0
Factor 2 out of -6p.
2(p2)+2(-3p)+20=0
Factor 2 out of 20.
2p2+2(-3p)+2⋅10=0
Factor 2 out of 2p2+2(-3p).
2(p2-3p)+2⋅10=0
Factor 2 out of 2(p2-3p)+2⋅10.
2(p2-3p+10)=0
2(p2-3p+10)=0
Divide each term by 2 and simplify.
Divide each term in 2(p2-3p+10)=0 by 2.
2(p2-3p+10)2=02
Cancel the common factor of 2.
Cancel the common factor.
2(p2-3p+10)2=02
Divide p2-3p+10 by 1.
p2-3p+10=02
p2-3p+10=02
Divide 0 by 2.
p2-3p+10=0
p2-3p+10=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-3, and c=10 into the quadratic formula and solve for p.
3±(-3)2-4⋅(1⋅10)2⋅1
Simplify.
Simplify the numerator.
Raise -3 to the power of 2.
p=3±9-4⋅(1⋅10)2⋅1
Multiply 10 by 1.
p=3±9-4⋅102⋅1
Multiply -4 by 10.
p=3±9-402⋅1
Subtract 40 from 9.
p=3±-312⋅1
Rewrite -31 as -1(31).
p=3±-1⋅312⋅1
Rewrite -1(31) as -1⋅31.
p=3±-1⋅312⋅1
Rewrite -1 as i.
p=3±i312⋅1
p=3±i312⋅1
Multiply 2 by 1.
p=3±i312
p=3±i312
The final answer is the combination of both solutions.
p=3+i312,3-i312
Solve for p 2p^2=6p-20

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