What are the solutions to the equation ((1))/((9))x^2-((1))/((3))x+((1))/((4))=0 ?

The solutions to the equation ((1))/((9))x^2-((1))/((3))x+((1))/((4))=0 are x= 3/2

Find the zeros of ((1))/((9))x^2-((1))/((3))x+((1))/((4))=0

The zeros of ((1))/((9))x^2-((1))/((3))x+((1))/((4))=0 are x= 3/2

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\frac{( 1 )}{( 9 )} x^{2} - \frac{( 1 )}{( 3 )} x + \frac{( 1 )}{( 4 )} = 0

x = \frac{3}{2}

Decimal Notation

x = 1.5

Solution steps

\frac{( 1 )}{( 9 )} x^{2} - \frac{( 1 )}{( 3 )} x + \frac{( 1 )}{( 4 )} = 0

Simplify

(4) : 4

\frac{( 1 )}{( 9 )} x^{2} - \frac{( 1 )}{( 3 )} x + \frac{( 1 )}{4} = 0

Find Least Common Multiplier of

9, 3, 4 : 36

Multiply by LCM=

36

\frac{1}{9} x^{2} \cdot 36 - \frac{1}{3} x \cdot 36 + \frac{1}{4} \cdot 36 = 0 \cdot 36

Simplify

4 x^{2} - 12 x + 9 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 4 \cdot 9}{2 \cdot 4}

(- 12)^{2} - 4 \cdot 4 \cdot 9 = 0

x_{1, 2} = \frac{- ( - 12 ) \pm 0}{2 \cdot 4}

x = \frac{- ( - 12 )}{2 \cdot 4}

\frac{- ( - 12 )}{2 \cdot 4} = \frac{3}{2}

x = \frac{3}{2}

The solution to the quadratic equation is:

x = \frac{3}{2}

2 y^{2} + y - 4 = 0

x^{2} - 12 x + 30 = - 2

6 = x 2

\frac{y}{x ^{2} - 1} \cdot \frac{x - 1}{2 y}

\frac{( a ^{2} + b ) ^{\frac{3}{2}}}{a ^{2} + b}

What are the solutions to the equation ((1))/((9))x^2-((1))/((3))x+((1))/((4))=0 ?
The solutions to the equation ((1))/((9))x^2-((1))/((3))x+((1))/((4))=0 are x= 3/2
Find the zeros of ((1))/((9))x^2-((1))/((3))x+((1))/((4))=0
The zeros of ((1))/((9))x^2-((1))/((3))x+((1))/((4))=0 are x= 3/2