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\[-6{x}^{2}=5x+9\]
+
−
.
ln
>
<
×
÷
/
log
≥
≤
(
)
log
x
=
%
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"(x+1)/2+4=7"
"factor x^2+5x+6"
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-6x^2=5x+9
-6x^2=5x+9
-{6x}^{2}=5x+9
1
Move all terms to one side.
6
x
2
+
5
x
+
9
=
0
6{x}^{2}+5x+9=0
6
x
2
+
5
x
+
9
=
0
2
Use the Quadratic Formula.
1
In general, given
a
x
2
+
b
x
+
c
=
0
a{x}^{2}+bx+c=0
a
x
2
+
b
x
+
c
=
0
, there exists two solutions where:
x
=
−
b
+
b
2
−
4
a
c
2
a
,
−
b
−
b
2
−
4
a
c
2
a
x=\frac{-b+\sqrt{{b}^{2}-4ac}}{2a},\frac{-b-\sqrt{{b}^{2}-4ac}}{2a}
x
=
2
a
−
b
+
b
2
−
4
a
c
,
2
a
−
b
−
b
2
−
4
a
c
2
In this case,
a
=
6
a=6
a
=
6
,
b
=
5
b=5
b
=
5
and
c
=
9
c=9
c
=
9
.
x
=
−
5
+
5
2
−
4
×
6
×
9
2
×
6
,
−
5
−
5
2
−
4
×
6
×
9
2
×
6
{x}^{}=\frac{-5+\sqrt{{5}^{2}-4\times 6\times 9}}{2\times 6},\frac{-5-\sqrt{{5}^{2}-4\times 6\times 9}}{2\times 6}
x
=
2
×
6
−
5
+
5
2
−
4
×
6
×
9
,
2
×
6
−
5
−
5
2
−
4
×
6
×
9
3
Simplify.
x
=
−
5
+
191
ı
12
,
−
5
−
191
ı
12
x=\frac{-5+\sqrt{191}\imath }{12},\frac{-5-\sqrt{191}\imath }{12}
x
=
1
2
−
5
+
1
9
1
,
1
2
−
5
−
1
9
1
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x
=
−
5
+
191
ı
12
,
−
5
−
191
ı
12
x=\frac{-5+\sqrt{191}\imath }{12},\frac{-5-\sqrt{191}\imath }{12}
x
=
1
2
−
5
+
1
9
1
,
1
2
−
5
−
1
9
1
Done
x=(-5+sqrt(191)*IM)/12,(-5-sqrt(191)*IM)/12
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