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Popular >

x^2+7/3-(x^2-3)/9 =3x+1

Solution

x^{2} + \frac{7}{3} - \frac{x ^{2} - 3}{9} = 3 x + 1

Solution

x = \frac{27 + 249}{16}, x = \frac{27 - 249}{16}

+1

Decimal

x = 2.67373 \dots, x = 0.70126 \dots

Solution steps

x^{2} + \frac{7}{3} - \frac{x ^{2} - 3}{9} = 3 x + 1

Find Least Common Multiplier of

3, 9 : 9

Multiply by LCM=

9

x^{2} \cdot 9 + \frac{7}{3} \cdot 9 - \frac{x ^{2} - 3}{9} \cdot 9 = 3 x \cdot 9 + 1 \cdot 9

Simplify

9 x^{2} + 21 - (x^{2} - 3) = 27 x + 9

Expand

9 x^{2} + 21 - (x^{2} - 3) : 8 x^{2} + 24

8 x^{2} + 24 = 27 x + 9

Move

9

to the left side

8 x^{2} + 15 = 27 x

Move

27 x

to the left side

8 x^{2} + 15 - 27 x = 0

Write in the standard form

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

8 x^{2} - 27 x + 15 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 27 ) \pm ( - 27 ) ^{2} - 4 \cdot 8 \cdot 15}{2 \cdot 8}

(- 27)^{2} - 4 \cdot 8 \cdot 15 = 249

x_{1, 2} = \frac{- ( - 27 ) \pm 249}{2 \cdot 8}

Separate the solutions

x_{1} = \frac{- ( - 27 ) + 249}{2 \cdot 8}, x_{2} = \frac{- ( - 27 ) - 249}{2 \cdot 8}

x = \frac{- ( - 27 ) + 249}{2 \cdot 8} : \frac{27 + 249}{16}

x = \frac{- ( - 27 ) - 249}{2 \cdot 8} : \frac{27 - 249}{16}

The solutions to the quadratic equation are:

x = \frac{27 + 249}{16}, x = \frac{27 - 249}{16}

Graph

Popular Examples

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- 6 x^{2} + 66 x - 168 = 0

\frac{x ^{2}}{2} + 4 x = 24

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