What are the solutions to the equation 3x^2-4x+5=2x+3 ?

The solutions to the equation 3x^2-4x+5=2x+3 are x=(3+sqrt(3))/3 ,x=(3-sqrt(3))/3

Find the zeros of 3x^2-4x+5=2x+3

The zeros of 3x^2-4x+5=2x+3 are x=(3+sqrt(3))/3 ,x=(3-sqrt(3))/3

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3 x^{2} - 4 x + 5 = 2 x + 3

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

Decimal Notation

x = 1.57735 \dots, x = 0.42264 \dots

Solution steps

3 x^{2} - 4 x + 5 = 2 x + 3

Move

3

to the left side

3 x^{2} - 4 x + 2 = 2 x

Move

2 x

to the left side

3 x^{2} - 6 x + 2 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 3 \cdot 2}{2 \cdot 3}

(- 6)^{2} - 4 \cdot 3 \cdot 2 = 23

x_{1, 2} = \frac{- ( - 6 ) \pm 2 3}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 2 3}{2 \cdot 3}, x_{2} = \frac{- ( - 6 ) - 2 3}{2 \cdot 3}

x = \frac{- ( - 6 ) + 2 3}{2 \cdot 3} : \frac{3 + 3}{3}

x = \frac{- ( - 6 ) - 2 3}{2 \cdot 3} : \frac{3 - 3}{3}

The solutions to the quadratic equation are:

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

6 + x - x^{2}

x^{2} = - 7 x

x^{2} + 2 x - 15 > 0

- \frac{π}{6} + \frac{π}{2}

4 (x + 1) = 16

What are the solutions to the equation 3x^2-4x+5=2x+3 ?
The solutions to the equation 3x^2-4x+5=2x+3 are x=(3+sqrt(3))/3 ,x=(3-sqrt(3))/3
Find the zeros of 3x^2-4x+5=2x+3
The zeros of 3x^2-4x+5=2x+3 are x=(3+sqrt(3))/3 ,x=(3-sqrt(3))/3