What are the solutions to the equation 5x=3x^2-9x+12 ?

The solutions to the equation 5x=3x^2-9x+12 are x=(7+sqrt(13))/3 ,x=(7-sqrt(13))/3

Find the zeros of 5x=3x^2-9x+12

The zeros of 5x=3x^2-9x+12 are x=(7+sqrt(13))/3 ,x=(7-sqrt(13))/3

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5 x = 3 x^{2} - 9 x + 12

x = \frac{7 + 13}{3}, x = \frac{7 - 13}{3}

Decimal Notation

x = 3.53518 \dots, x = 1.13148 \dots

Solution steps

5 x = 3 x^{2} - 9 x + 12

Switch sides

3 x^{2} - 9 x + 12 = 5 x

Move

5 x

to the left side

3 x^{2} - 14 x + 12 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 14 ) \pm ( - 14 ) ^{2} - 4 \cdot 3 \cdot 12}{2 \cdot 3}

(- 14)^{2} - 4 \cdot 3 \cdot 12 = 213

x_{1, 2} = \frac{- ( - 14 ) \pm 2 13}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 14 ) + 2 13}{2 \cdot 3}, x_{2} = \frac{- ( - 14 ) - 2 13}{2 \cdot 3}

x = \frac{- ( - 14 ) + 2 13}{2 \cdot 3} : \frac{7 + 13}{3}

x = \frac{- ( - 14 ) - 2 13}{2 \cdot 3} : \frac{7 - 13}{3}

The solutions to the quadratic equation are:

x = \frac{7 + 13}{3}, x = \frac{7 - 13}{3}

(2 x - 4)^{2} = 32

3 x^{2} - 4 x + 9 = 10 x + 3

x^{2} - 14 x = 6

y, 2 x^{2} - 3 y^{2} + 5 x y - 2 x + 3 y - 4 = 0

4 x^{2} + 7 mn x - 15 m^{2} n^{2}

What are the solutions to the equation 5x=3x^2-9x+12 ?
The solutions to the equation 5x=3x^2-9x+12 are x=(7+sqrt(13))/3 ,x=(7-sqrt(13))/3
Find the zeros of 5x=3x^2-9x+12
The zeros of 5x=3x^2-9x+12 are x=(7+sqrt(13))/3 ,x=(7-sqrt(13))/3