What are the solutions to the equation (x^2)/3 = 11/6 x+1 ?

The solutions to the equation (x^2)/3 = 11/6 x+1 are x=6,x=-1/2

Find the zeros of (x^2)/3 = 11/6 x+1

The zeros of (x^2)/3 = 11/6 x+1 are x=6,x=-1/2

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\frac{x ^{2}}{3} = \frac{11}{6} x + 1

x = 6, x = - \frac{1}{2}

Decimal Notation

x = 6, x = - 0.5

Solution steps

\frac{x ^{2}}{3} = \frac{11}{6} x + 1

Find Least Common Multiplier of

3, 6 : 6

Multiply by LCM=

6

\frac{x ^{2}}{3} \cdot 6 = \frac{11}{6} x \cdot 6 + 1 \cdot 6

Simplify

2 x^{2} = 11 x + 6

Move

6

to the left side

2 x^{2} - 6 = 11 x

Move

11 x

to the left side

2 x^{2} - 6 - 11 x = 0

Write in the standard form

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

2 x^{2} - 11 x - 6 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 11 ) \pm ( - 11 ) ^{2} - 4 \cdot 2 ( - 6 )}{2 \cdot 2}

(- 11)^{2} - 4 \cdot 2 (- 6) = 13

x_{1, 2} = \frac{- ( - 11 ) \pm 13}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 11 ) + 13}{2 \cdot 2}, x_{2} = \frac{- ( - 11 ) - 13}{2 \cdot 2}

x = \frac{- ( - 11 ) + 13}{2 \cdot 2} : 6

x = \frac{- ( - 11 ) - 13}{2 \cdot 2} : - \frac{1}{2}

The solutions to the quadratic equation are:

x = 6, x = - \frac{1}{2}

(k + 2) x^{2} + 5 x - 3 = 0

(x + 2)^{2} - 36 = 0

t^{2} - 36 = 0

\frac{X ^{2}}{64} - \frac{X ^{2}}{9} = 1

x^{2} + 6

What are the solutions to the equation (x^2)/3 = 11/6 x+1 ?
The solutions to the equation (x^2)/3 = 11/6 x+1 are x=6,x=-1/2
Find the zeros of (x^2)/3 = 11/6 x+1
The zeros of (x^2)/3 = 11/6 x+1 are x=6,x=-1/2