Step-by-step explanation:
x−
3
6
=
x
9
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3x, the least common multiple of 3,x.
3xx−x×6=3×9
Multiply x and x to get x
2
.
3x
2
−x×6=3×9
Multiply 3 and 9 to get 27.
Subtract 27 from both sides.
3x
2
−x×6−27=0
Multiply −1 and 6 to get −6.
3x
2
−6x−27=0
This equation is in standard form: ax
2
+bx+c=0. Substitute 3 for a, −6 for b, and −27 for c in the quadratic formula,
2a
−b±
b
2
−4ac
. 2×3
−(−6)±
(−6)
2
−4×3(−27)
Square −6.
x=
2×3
−(−6)±
36−4×3(−27)
Multiply −4 times 3.
x=
2×3
−(−6)±
36−12(−27)
Multiply −12 times −27.
x=
2×3
−(−6)±
36+324
Add 36 to 324.
x=
2×3
−(−6)±
360
Take the square root of 360.
x=
2×3
−(−6)±6
10
The opposite of −6 is 6.
x=
2×3
6±6
10
Multiply 2 times 3.
x=
6
6±6
10
Now solve the equation x=
6
6±6
10
when ± is plus. Add 6 to 6
10
.
x=
6
6
10
+6
Divide 6+6
10
by 6.
x=
10
+1
Now solve the equation x=
6
6±6
10
when ± is minus. Subtract 6
10
from 6.
x=
6
6−6
10
Divide 6−6
10
by 6.
x=1−
10
The equation is now solved.
x=
10
+1
x=1−
10
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