What are the solutions to the equation x/2+3x(x-1)=38 ?

The solutions to the equation x/2+3x(x-1)=38 are x=4,x=-19/6

Find the zeros of x/2+3x(x-1)=38

The zeros of x/2+3x(x-1)=38 are x=4,x=-19/6

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\frac{x}{2} + 3 x (x - 1) = 38

x = 4, x = - \frac{19}{6}

Decimal Notation

x = 4, x = - 3.16666 \dots

Solution steps

\frac{x}{2} + 3 x (x - 1) = 38

Multiply both sides by

2

x + 6 x (x - 1) = 76

Expand

x + 6 x (x - 1) : 6 x^{2} - 5 x

6 x^{2} - 5 x = 76

Move

76

to the left side

6 x^{2} - 5 x - 76 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 6 ( - 76 )}{2 \cdot 6}

(- 5)^{2} - 4 \cdot 6 (- 76) = 43

x_{1, 2} = \frac{- ( - 5 ) \pm 43}{2 \cdot 6}

Separate the solutions

x_{1} = \frac{- ( - 5 ) + 43}{2 \cdot 6}, x_{2} = \frac{- ( - 5 ) - 43}{2 \cdot 6}

x = \frac{- ( - 5 ) + 43}{2 \cdot 6} : 4

x = \frac{- ( - 5 ) - 43}{2 \cdot 6} : - \frac{19}{6}

The solutions to the quadratic equation are:

x = 4, x = - \frac{19}{6}

7 - \frac{x}{3} > 8

x^{2} - 8 = - 1

- 13 x + 12 = 13 x - 13

\frac{3}{4 ^{3}}

2 g + 1 \geq 9

What are the solutions to the equation x/2+3x(x-1)=38 ?
The solutions to the equation x/2+3x(x-1)=38 are x=4,x=-19/6
Find the zeros of x/2+3x(x-1)=38
The zeros of x/2+3x(x-1)=38 are x=4,x=-19/6