What are the solutions to the equation 5x^2-57x=3x-120 ?

The solutions to the equation 5x^2-57x=3x-120 are x=2(3+sqrt(3)),x=2(3-sqrt(3))

Find the zeros of 5x^2-57x=3x-120

The zeros of 5x^2-57x=3x-120 are x=2(3+sqrt(3)),x=2(3-sqrt(3))

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5 x^{2} - 57 x = 3 x - 120

x = 2 (3 + 3), x = 2 (3 - 3)

Decimal Notation

x = 9.46410 \dots, x = 2.53589 \dots

Solution steps

5 x^{2} - 57 x = 3 x - 120

Move

120

to the left side

5 x^{2} - 57 x + 120 = 3 x

Move

3 x

to the left side

5 x^{2} - 60 x + 120 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 60 ) \pm ( - 60 ) ^{2} - 4 \cdot 5 \cdot 120}{2 \cdot 5}

(- 60)^{2} - 4 \cdot 5 \cdot 120 = 203

x_{1, 2} = \frac{- ( - 60 ) \pm 20 3}{2 \cdot 5}

Separate the solutions

x_{1} = \frac{- ( - 60 ) + 20 3}{2 \cdot 5}, x_{2} = \frac{- ( - 60 ) - 20 3}{2 \cdot 5}

x = \frac{- ( - 60 ) + 20 3}{2 \cdot 5} : 2 (3 + 3)

x = \frac{- ( - 60 ) - 20 3}{2 \cdot 5} : 2 (3 - 3)

The solutions to the quadratic equation are:

x = 2 (3 + 3), x = 2 (3 - 3)

(2 - x)^{2} = 0

121 - x^{2} = 0

- 3 x^{2} - 63 x - 194 = - 15 x + 1

x^{2} + 66 = 14 x + 15

- 4 x^{2} + 40 x - 120 = 0

What are the solutions to the equation 5x^2-57x=3x-120 ?
The solutions to the equation 5x^2-57x=3x-120 are x=2(3+sqrt(3)),x=2(3-sqrt(3))
Find the zeros of 5x^2-57x=3x-120
The zeros of 5x^2-57x=3x-120 are x=2(3+sqrt(3)),x=2(3-sqrt(3))