# Solve for n 3n^2+9n=363 3n2+9n=363
Move 363 to the left side of the equation by subtracting it from both sides.
3n2+9n-363=0
Factor 3 out of 3n2+9n-363.
Factor 3 out of 3n2.
3(n2)+9n-363=0
Factor 3 out of 9n.
3(n2)+3(3n)-363=0
Factor 3 out of -363.
3n2+3(3n)+3⋅-121=0
Factor 3 out of 3n2+3(3n).
3(n2+3n)+3⋅-121=0
Factor 3 out of 3(n2+3n)+3⋅-121.
3(n2+3n-121)=0
3(n2+3n-121)=0
Divide each term by 3 and simplify.
Divide each term in 3(n2+3n-121)=0 by 3.
3(n2+3n-121)3=03
Cancel the common factor of 3.
Cancel the common factor.
3(n2+3n-121)3=03
Divide n2+3n-121 by 1.
n2+3n-121=03
n2+3n-121=03
Divide 0 by 3.
n2+3n-121=0
n2+3n-121=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=3, and c=-121 into the quadratic formula and solve for n.
-3±32-4⋅(1⋅-121)2⋅1
Simplify.
Simplify the numerator.
Raise 3 to the power of 2.
n=-3±9-4⋅(1⋅-121)2⋅1
Multiply -121 by 1.
n=-3±9-4⋅-1212⋅1
Multiply -4 by -121.
n=-3±9+4842⋅1
Add 9 and 484.
n=-3±4932⋅1
n=-3±4932⋅1
Multiply 2 by 1.
n=-3±4932
n=-3±4932
The final answer is the combination of both solutions.
n=-3-4932,-3+4932
The result can be shown in multiple forms.
Exact Form:
n=-3-4932,-3+4932
Decimal Form:
n=9.60180165…,-12.60180165…
Solve for n 3n^2+9n=363

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