The Quadratic formula provides the solution for
A
x
2
+
B
x
+
C
=
0
, in which A, B and C are numbers (or coefficients), as follows:
−
b
±
b
2
−
4
a
c
2
a
2. Determine the quadratic equation’s coefficients A, B and C
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The coefficients of our equation,
3
x
2
−
1
x
−
5
=
0
, are:
A = 3
B = -1
C = -5
3. Plug these coefficients into the quadratic formula
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−
b
±
b
2
−
4
a
c
2
a
=
−
1
⋅
−
1
±
−
1
2
−
4
⋅
3
⋅
−
5
2
⋅
3
Simplify exponents and square roots.
−
1
⋅
−
1
±
−
1
2
−
4
⋅
3
⋅
−
5
2
⋅
3
−
1
⋅
−
1
±
1
−
4
⋅
3
⋅
−
5
2
⋅
3
Perform any multiplication or division, from left to right.
−
1
⋅
−
1
±
1
−
12
⋅
−
5
2
⋅
3
−
1
⋅
−
1
±
1
−
−
60
2
⋅
3
−
1
⋅
−
1
±
61
2
⋅
3
−
1
⋅
−
1
±
61
6
1
±
61
6
to get the result:
x
=
1
±
61
6
4. Solve the equation for x
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x
=
1
±
61
6
The ± means two answers are possible:
x
=
1.4683749459844417
or:
x
=
−
1.1350416126511085
Separate the equations.
x
=
1
+
61
6
and
x
=
1
−
61
6
We first calculate the expressions inside the parentheses from left to right and from inner to outer.
x
=
1
+
61
6
x
=
1
+
7.810249675906654
6
x
=
8.81024967590665
6
x
=
1.4683749459844417
We first calculate the expressions inside the parentheses from left to right and from inner to outer.
x
=
1
−
61
6
x
=
1
−
7.810249675906654
6
x
=
−
6.81024967590665
6
x
=
−
1.1350416126511085
