solve x: 6x2 +5x-4=0
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Step-by-step explanation:
We can Split the Middle Term of this expression to factorise it and thereby find solutions.
In this technique, if we have to factorise an expression like
a
x
2
+
b
x
+
c
, we need to think of 2 numbers such that:
N
1
⋅
N
2
=
a
⋅
c
=
6
⋅
−
4
=
−
24
and
N
1
+
N
2
=
b
=
5
After trying out a few numbers we get
N
1
=
8
and
N
2
=
−
3
8
⋅
−
3
=
−
24
, and
8
+
(
−
3
)
=
5
6
x
2
+
5
x
−
4
=
6
x
2
−
3
x
+
8
x
−
4
=
3
x
(
2
x
−
1
)
+
4
(
2
x
−
1
)
=
0
=
(
3
x
+
4
)
(
2
x
−
1
)
=
0
Now we equate the factors to zero.
=
3
x
+
4
=
0
,
x
=
−
4
3
=
2
x
−
1
=
0
,
x
=
1
2
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