What are the solutions to the equation 2X(X-1)=4X-3 ?

The solutions to the equation 2X(X-1)=4X-3 are X=(3+sqrt(3))/2 ,X=(3-sqrt(3))/2

Find the zeros of 2X(X-1)=4X-3

The zeros of 2X(X-1)=4X-3 are X=(3+sqrt(3))/2 ,X=(3-sqrt(3))/2

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2 X (X - 1) = 4 X - 3

X = \frac{3 + 3}{2}, X = \frac{3 - 3}{2}

Decimal Notation

X = 2.36602 \dots, X = 0.63397 \dots

Solution steps

2 X (X - 1) = 4 X - 3

Expand

2 X (X - 1) : 2 X^{2} - 2 X

2 X^{2} - 2 X = 4 X - 3

Move

3

to the left side

2 X^{2} - 2 X + 3 = 4 X

Move

4 X

to the left side

2 X^{2} - 6 X + 3 = 0

Solve with the quadratic formula

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

(- 6)^{2} - 4 \cdot 2 \cdot 3 = 23

X_{1, 2} = \frac{- ( - 6 ) \pm 2 3}{2 \cdot 2}

Separate the solutions

X_{1} = \frac{- ( - 6 ) + 2 3}{2 \cdot 2}, X_{2} = \frac{- ( - 6 ) - 2 3}{2 \cdot 2}

X = \frac{- ( - 6 ) + 2 3}{2 \cdot 2} : \frac{3 + 3}{2}

X = \frac{- ( - 6 ) - 2 3}{2 \cdot 2} : \frac{3 - 3}{2}

The solutions to the quadratic equation are:

X = \frac{3 + 3}{2}, X = \frac{3 - 3}{2}

5 x^{2} - 9 = 4 x

5 y - 6 + 50 y^{2} = 0

0 = 4 x^{2} - 5 x - 3

2 x^{2} + 6 x + 3 = 3

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

What are the solutions to the equation 2X(X-1)=4X-3 ?
The solutions to the equation 2X(X-1)=4X-3 are X=(3+sqrt(3))/2 ,X=(3-sqrt(3))/2
Find the zeros of 2X(X-1)=4X-3
The zeros of 2X(X-1)=4X-3 are X=(3+sqrt(3))/2 ,X=(3-sqrt(3))/2