What are the solutions to the equation -3/2 x^2-12x+54=0 ?

The solutions to the equation -3/2 x^2-12x+54=0 are x=-2(2+sqrt(13)),x=2(sqrt(13)-2)

Find the zeros of -3/2 x^2-12x+54=0

The zeros of -3/2 x^2-12x+54=0 are x=-2(2+sqrt(13)),x=2(sqrt(13)-2)

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- \frac{3}{2} x^{2} - 12 x + 54 = 0

x = - 2 (2 + 13), x = 2 (13 - 2)

Decimal Notation

x = - 11.21110 \dots, x = 3.21110 \dots

Solution steps

- \frac{3}{2} x^{2} - 12 x + 54 = 0

Multiply both sides by

2

- 3 x^{2} - 24 x + 108 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 24 ) \pm ( - 24 ) ^{2} - 4 ( - 3 ) \cdot 108}{2 ( - 3 )}

(- 24)^{2} - 4 (- 3) \cdot 108 = 1213

x_{1, 2} = \frac{- ( - 24 ) \pm 12 13}{2 ( - 3 )}

Separate the solutions

x_{1} = \frac{- ( - 24 ) + 12 13}{2 ( - 3 )}, x_{2} = \frac{- ( - 24 ) - 12 13}{2 ( - 3 )}

x = \frac{- ( - 24 ) + 12 13}{2 ( - 3 )} : - 2 (2 + 13)

x = \frac{- ( - 24 ) - 12 13}{2 ( - 3 )} : 2 (13 - 2)

The solutions to the quadratic equation are:

x = - 2 (2 + 13), x = 2 (13 - 2)

- 3 x^{2} - 10 x + 16 = 0

8 x^{2} + 22 x + 15 = 0

- 16 t^{2} + 10 t + 6 = 0

x, 9 x^{2} - 4 y^{2} + 36 x + 24 y = 0

2 x^{2} + 8 x + 4

What are the solutions to the equation -3/2 x^2-12x+54=0 ?
The solutions to the equation -3/2 x^2-12x+54=0 are x=-2(2+sqrt(13)),x=2(sqrt(13)-2)
Find the zeros of -3/2 x^2-12x+54=0
The zeros of -3/2 x^2-12x+54=0 are x=-2(2+sqrt(13)),x=2(sqrt(13)-2)