-\frac{1}{2}n^{2}+18=0

−
1
2
⋅

2
+
1
8
=
0
Combine multiplied terms into a single fraction
−
1
2

2
+
1
8
=
0
−
1

2
2
+
1
8
=
0

Multiply all terms by the same value to eliminate fraction denominators
−
1

2
2
+
1
8
=
0
2
(
−
1

2
2
+
1
8
)
=
2
⋅
0

Simplify
Distribute
2
(
−
1

2
2
+
1
8
)
=
2
⋅
0
2
(
−
1
n
2
2
+
18
)
=
2
⋅
0
2(2−1n2​+18)=2⋅0
2
⋅
−
1

2
2
+
3
6
=
2
⋅
0
2
⋅
−
1
n
2
2
+
36
=
2
⋅
0
2⋅2−1n2​+36=2⋅0

Cancel multiplied terms that are in the denominator
2
⋅
−
1

2
2
+
3
6
=
2
⋅
0
2
⋅
−
1
n
2
2
+
36
=
2
⋅
0
2​⋅2​−1n2​+36=2⋅0
−
1

2
+
3
6
=
2
⋅
0

Multiply by zero
−
1

2
+
3
6
=
2
⋅
0
−
1
n
2
+
36
=
2
⋅
0
−1n2+36=2⋅0
−
1

2
+
3
6
=
0
−
1
n
2
+
36
=
0
−1n2+36=0
−
1

2
+
3
6
=
0

=
−

±

2
−
4

√
2

n
=
−
b
±
b
2
−
4
a
c
2
a
n=2a−b±b2−4ac​​
Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.
−
1

2
+
3
6
=
0
−
1
n
2
+
36
=
0
−1n2+36=0

=
−
1
a
=
−
1
a=−1

=
0
b
=
0
b=0

=
3
6
c
=
36
c=36

=
−
0
±
0
2
−
4
(
−
1
)
⋅
3
6
√
2
(
−
1
)

Simplify
Evaluate the exponent

=
0
±
0
2
−
4
(
−
1
)
⋅
3
6
√
2
(
−
1
)
n
=
0
±
0
2
−
4
(
−
1
)
⋅
36
2
(
−
1
)
n=2(−1)0±02−4(−1)⋅36​​

=
0
±
0
−
4
(
−
1
)
⋅
3
6
√
2
(
−
1
)

Multiply the numbers

=
0
±
0
−
4
(
−
1
)
⋅
3
6
√
2
(
−
1
)
n
=
0
±
0
−
4
(
−
1
)
⋅
36
2
(
−
1
)
n=2(−1)0±0−4(−1)⋅36​​

=
0
±
0
+
1
4
4
√
2
(
−
1
)

Add the numbers

=
0
±
0
+
1
4
4
√
2
(
−
1
)
n
=
0
±
0
+
144
2
(
−
1
)
n=2(−1)0±0+144​​

=
0
±
1
4
4
√
2
(
−
1
)

Evaluate the square root

=
0
±
1
4
4
√
2
(
−
1
)
n
=
0
±
144
2
(
−
1
)
n=2(−1)0±144​​

=
0
±
1
2
2
(
−
1
)

Multiply the numbers

=
0
±
1
2
2
(
−
1
)
n
=
0
±
12
2
(
−
1
)
n=2(−1)0±12​

=
0
±
1
2
−
2
n
=
0
±
12
−
2
n=−20±12​

=
0
±
1
2
−
2

Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

=
0
+
1
2
−
2

=
0
−
1
2
−
2

Solve
Rearrange and isolate the variable to find each solution

=
−
6

=
6

Solution

=
−
6

=
6

Hope it helps u:) ps have a great day (taken from Google)