What are the solutions to the equation 2/3 x-1/2 x= 3/4 x^2 ?

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

Find the zeros of 2/3 x-1/2 x= 3/4 x^2

The zeros of 2/3 x-1/2 x= 3/4 x^2 are x= 2/9 ,x=0

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\frac{2}{3} x - \frac{1}{2} x = \frac{3}{4} x^{2}

x = \frac{2}{9}, x = 0

Decimal Notation

x = 0.22222 \dots, x = 0

Solution steps

\frac{2}{3} x - \frac{1}{2} x = \frac{3}{4} x^{2}

Find Least Common Multiplier of

3, 2, 4 : 12

Multiply by LCM=

12

\frac{2}{3} x \cdot 12 - \frac{1}{2} x \cdot 12 = \frac{3}{4} x^{2} \cdot 12

Simplify

8 x - 6 x = 9 x^{2}

2 x = 9 x^{2}

Switch sides

9 x^{2} = 2 x

Move

2 x

to the left side

9 x^{2} - 2 x = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 9 \cdot 0}{2 \cdot 9}

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

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

Separate the solutions

x_{1} = \frac{- ( - 2 ) + 2}{2 \cdot 9}, x_{2} = \frac{- ( - 2 ) - 2}{2 \cdot 9}

x = \frac{- ( - 2 ) + 2}{2 \cdot 9} : \frac{2}{9}

x = \frac{- ( - 2 ) - 2}{2 \cdot 9} : 0

The solutions to the quadratic equation are:

x = \frac{2}{9}, x = 0

9 x^{2} + 8 x + 2 = 0

0.12 q^{2} + 200 = - 10 q + 1000

7 x^{2} - 21 x - 28 = 0

a, f (a + h) = 3 (a + h)^{2} + 5 (a + h) - 2

(x - 6)^{2} = 2 (x + 18)

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