How do i work out 3x²+x-5=0

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