What are the solutions to the equation 3x^2=2x+3 ?

The solutions to the equation 3x^2=2x+3 are x=(1+sqrt(10))/3 ,x=(1-sqrt(10))/3

Find the zeros of 3x^2=2x+3

The zeros of 3x^2=2x+3 are x=(1+sqrt(10))/3 ,x=(1-sqrt(10))/3

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3 x^{2} = 2 x + 3

x = \frac{1 + 10}{3}, x = \frac{1 - 10}{3}

Decimal Notation

x = 1.38742 \dots, x = - 0.72075 \dots

Solution steps

3 x^{2} = 2 x + 3

Move

3

to the left side

3 x^{2} - 3 = 2 x

Move

2 x

to the left side

3 x^{2} - 3 - 2 x = 0

Write in the standard form

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

3 x^{2} - 2 x - 3 = 0

Solve with the quadratic formula

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

(- 2)^{2} - 4 \cdot 3 (- 3) = 210

x_{1, 2} = \frac{- ( - 2 ) \pm 2 10}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 2 ) + 2 10}{2 \cdot 3}, x_{2} = \frac{- ( - 2 ) - 2 10}{2 \cdot 3}

x = \frac{- ( - 2 ) + 2 10}{2 \cdot 3} : \frac{1 + 10}{3}

x = \frac{- ( - 2 ) - 2 10}{2 \cdot 3} : \frac{1 - 10}{3}

The solutions to the quadratic equation are:

x = \frac{1 + 10}{3}, x = \frac{1 - 10}{3}

4 x + 34 = 106

2 (\frac{5 - y}{3}) - 3 y = 7

r - 13 = 3

x^{2} - 8 x y - 20 y^{2}

\frac{( 2 x )}{( \frac{3 x y}{5} )}

What are the solutions to the equation 3x^2=2x+3 ?
The solutions to the equation 3x^2=2x+3 are x=(1+sqrt(10))/3 ,x=(1-sqrt(10))/3
Find the zeros of 3x^2=2x+3
The zeros of 3x^2=2x+3 are x=(1+sqrt(10))/3 ,x=(1-sqrt(10))/3