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

The solutions to the equation 2x^2=4x+3 are x=(2+sqrt(10))/2 ,x=(2-sqrt(10))/2

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

The zeros of 2x^2=4x+3 are x=(2+sqrt(10))/2 ,x=(2-sqrt(10))/2

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2 x^{2} = 4 x + 3

x = \frac{2 + 10}{2}, x = \frac{2 - 10}{2}

Decimal Notation

x = 2.58113 \dots, x = - 0.58113 \dots

Solution steps

2 x^{2} = 4 x + 3

Move

3

to the left side

2 x^{2} - 3 = 4 x

Move

4 x

to the left side

2 x^{2} - 3 - 4 x = 0

Write in the standard form

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

2 x^{2} - 4 x - 3 = 0

Solve with the quadratic formula

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

(- 4)^{2} - 4 \cdot 2 (- 3) = 210

x_{1, 2} = \frac{- ( - 4 ) \pm 2 10}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 4 ) + 2 10}{2 \cdot 2}, x_{2} = \frac{- ( - 4 ) - 2 10}{2 \cdot 2}

x = \frac{- ( - 4 ) + 2 10}{2 \cdot 2} : \frac{2 + 10}{2}

x = \frac{- ( - 4 ) - 2 10}{2 \cdot 2} : \frac{2 - 10}{2}

The solutions to the quadratic equation are:

x = \frac{2 + 10}{2}, x = \frac{2 - 10}{2}

- 2 x^{2} - 8 x - 9 = 0

\frac{( x )}{( 2 )} = \frac{( x )}{( 6 )} - \frac{( 1 )}{( 4 )}

3 k^{2} - 18 k - 21 = 0

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

∣ x - 1 ∣ > ∣ 2 x - 1 ∣

What are the solutions to the equation 2x^2=4x+3 ?
The solutions to the equation 2x^2=4x+3 are x=(2+sqrt(10))/2 ,x=(2-sqrt(10))/2
Find the zeros of 2x^2=4x+3
The zeros of 2x^2=4x+3 are x=(2+sqrt(10))/2 ,x=(2-sqrt(10))/2