What are the solutions to the equation 3a-4=a(a-3) ?

The solutions to the equation 3a-4=a(a-3) are a=3+sqrt(5),a=3-sqrt(5)

Find the zeros of 3a-4=a(a-3)

The zeros of 3a-4=a(a-3) are a=3+sqrt(5),a=3-sqrt(5)

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3 a - 4 = a (a - 3)

a = 3 + 5, a = 3 - 5

Decimal Notation

a = 5.23606 \dots, a = 0.76393 \dots

Solution steps

3 a - 4 = a (a - 3)

Expand

a (a - 3) : a^{2} - 3 a

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

Switch sides

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

Move

4

to the left side

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

Move

3 a

to the left side

a^{2} - 6 a + 4 = 0

Solve with the quadratic formula

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

(- 6)^{2} - 4 \cdot 1 \cdot 4 = 25

a_{1, 2} = \frac{- ( - 6 ) \pm 2 5}{2 \cdot 1}

Separate the solutions

a_{1} = \frac{- ( - 6 ) + 2 5}{2 \cdot 1}, a_{2} = \frac{- ( - 6 ) - 2 5}{2 \cdot 1}

a = \frac{- ( - 6 ) + 2 5}{2 \cdot 1} : 3 + 5

a = \frac{- ( - 6 ) - 2 5}{2 \cdot 1} : 3 - 5

The solutions to the quadratic equation are:

a = 3 + 5, a = 3 - 5

3 z^{2} + 4 z + 5 = 0

(8 x + 3) (5 x - 7) = 0

5 u^{2} - 24 u - 5 = 0

- 4 x^{2} - 26 x + 190 = 6 x - 2

x^{2} + 0.000002 x - 0.0000004 = 0

What are the solutions to the equation 3a-4=a(a-3) ?
The solutions to the equation 3a-4=a(a-3) are a=3+sqrt(5),a=3-sqrt(5)
Find the zeros of 3a-4=a(a-3)
The zeros of 3a-4=a(a-3) are a=3+sqrt(5),a=3-sqrt(5)