What are the solutions to the equation (x^2)/2+(4x)/3 =6 ?

The solutions to the equation (x^2)/2+(4x)/3 =6 are x=(2(sqrt(31)-2))/3 ,x=-(2(2+sqrt(31)))/3

Find the zeros of (x^2)/2+(4x)/3 =6

The zeros of (x^2)/2+(4x)/3 =6 are x=(2(sqrt(31)-2))/3 ,x=-(2(2+sqrt(31)))/3

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\frac{x ^{2}}{2} + \frac{4 x}{3} = 6

x = \frac{2 ( 31 - 2 )}{3}, x = - \frac{2 ( 2 + 31 )}{3}

Decimal Notation

x = 2.37850 \dots, x = - 5.04517 \dots

Solution steps

\frac{x ^{2}}{2} + \frac{4 x}{3} = 6

Find Least Common Multiplier of

2, 3 : 6

Multiply by LCM=

6

\frac{x ^{2}}{2} \cdot 6 + \frac{4 x}{3} \cdot 6 = 6 \cdot 6

Simplify

3 x^{2} + 8 x = 36

Move

36

to the left side

3 x^{2} + 8 x - 36 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 8 \pm 8 ^{2} - 4 \cdot 3 ( - 36 )}{2 \cdot 3}

8^{2} - 4 \cdot 3 (- 36) = 431

x_{1, 2} = \frac{- 8 \pm 4 31}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- 8 + 4 31}{2 \cdot 3}, x_{2} = \frac{- 8 - 4 31}{2 \cdot 3}

x = \frac{- 8 + 4 31}{2 \cdot 3} : \frac{2 ( 31 - 2 )}{3}

x = \frac{- 8 - 4 31}{2 \cdot 3} : - \frac{2 ( 2 + 31 )}{3}

The solutions to the quadratic equation are:

x = \frac{2 ( 31 - 2 )}{3}, x = - \frac{2 ( 2 + 31 )}{3}

x^{2} + 9 x + 16 = 2 x + 6

5 x^{2} - 7 x + 4 = 0

9 x^{2} = 63 x

x^{2} - 2 x = 120

x^{2} - 29 x + 120 = 0

What are the solutions to the equation (x^2)/2+(4x)/3 =6 ?
The solutions to the equation (x^2)/2+(4x)/3 =6 are x=(2(sqrt(31)-2))/3 ,x=-(2(2+sqrt(31)))/3
Find the zeros of (x^2)/2+(4x)/3 =6
The zeros of (x^2)/2+(4x)/3 =6 are x=(2(sqrt(31)-2))/3 ,x=-(2(2+sqrt(31)))/3