x^2-93/216 x+53/1728 =0

Solution

x^{2} - \frac{93}{216} x + \frac{53}{1728} = 0

x = \frac{31 + 5 13}{144}, x = \frac{31 - 5 13}{144}

Decimal Notation

x = 0.34047 \dots, x = 0.09008 \dots

Solution steps

x^{2} - \frac{93}{216} x + \frac{53}{1728} = 0

Find Least Common Multiplier of

216, 1728 : 1728

Multiply by LCM=

1728

x^{2} \cdot 1728 - \frac{93}{216} x \cdot 1728 + \frac{53}{1728} \cdot 1728 = 0 \cdot 1728

Simplify

1728 x^{2} - 744 x + 53 = 0

Divide both sides by

1728

\frac{1728 x ^{2}}{1728} - \frac{744 x}{1728} + \frac{53}{1728} = \frac{0}{1728}

Write in the standard form

a x^{2} + b x + c = 0

x^{2} - \frac{31 x}{72} + \frac{53}{1728} = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - \frac{31}{72} ) \pm ( - \frac{31}{72} ) ^{2} - 4 \cdot 1 \cdot \frac{53}{1728}}{2 \cdot 1}

(- \frac{31}{72})^{2} - 4 \cdot 1 \cdot \frac{53}{1728} = \frac{5 13}{72}

x_{1, 2} = \frac{- ( - \frac{31}{72} ) \pm \frac{5 13}{72}}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - \frac{31}{72} ) + \frac{5 13}{72}}{2 \cdot 1}, x_{2} = \frac{- ( - \frac{31}{72} ) - \frac{5 13}{72}}{2 \cdot 1}

x = \frac{- ( - \frac{31}{72} ) + \frac{5 13}{72}}{2 \cdot 1} : \frac{31 + 5 13}{144}

x = \frac{- ( - \frac{31}{72} ) - \frac{5 13}{72}}{2 \cdot 1} : \frac{31 - 5 13}{144}

The solutions to the quadratic equation are:

x = \frac{31 + 5 13}{144}, x = \frac{31 - 5 13}{144}

- 2 x^{2} + 16 x - 28 = 0

(1 - 3 i)^{3}

(y + 1)^{2} = \frac{3}{2}

(2 x - 5)^{2} \geq 72 + (- 4 + x)^{2}

\frac{16}{9}