What are the solutions to the equation 2x^2-6=3x ?

The solutions to the equation 2x^2-6=3x are x=(3+sqrt(57))/4 ,x=(3-sqrt(57))/4

Find the zeros of 2x^2-6=3x

The zeros of 2x^2-6=3x are x=(3+sqrt(57))/4 ,x=(3-sqrt(57))/4

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2 x^{2} - 6 = 3 x

x = \frac{3 + 57}{4}, x = \frac{3 - 57}{4}

Decimal Notation

x = 2.63745 \dots, x = - 1.13745 \dots

Solution steps

2 x^{2} - 6 = 3 x

Move

3 x

to the left side

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

Write in the standard form

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

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

Solve with the quadratic formula

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

(- 3)^{2} - 4 \cdot 2 (- 6) = 57

x_{1, 2} = \frac{- ( - 3 ) \pm 57}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 57}{2 \cdot 2}, x_{2} = \frac{- ( - 3 ) - 57}{2 \cdot 2}

x = \frac{- ( - 3 ) + 57}{2 \cdot 2} : \frac{3 + 57}{4}

x = \frac{- ( - 3 ) - 57}{2 \cdot 2} : \frac{3 - 57}{4}

The solutions to the quadratic equation are:

x = \frac{3 + 57}{4}, x = \frac{3 - 57}{4}

5 x^{2} + x = - 5

7 x + 120 = x^{2}

2 a^{2} + 11 a - 21 = 0

3 x^{2} - \frac{1}{75} = 0

x^{2} = - 13 x

What are the solutions to the equation 2x^2-6=3x ?
The solutions to the equation 2x^2-6=3x are x=(3+sqrt(57))/4 ,x=(3-sqrt(57))/4
Find the zeros of 2x^2-6=3x
The zeros of 2x^2-6=3x are x=(3+sqrt(57))/4 ,x=(3-sqrt(57))/4