2x-6=x^2-3x — step-by-step solution

Let's solve in

ℝ

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

2 x

- 6

- x^{2}

+ 3 x = 0

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

Given the quadratic form

a x^{2} + b x + c

, you can calculate the discriminant:

Δ = b^{2} - 4 a c

Δ = 5^{2} - 4 \cdot (-1) \cdot (-6)

ℹ

5^{2}

25

‖

-4 \cdot (-1)

4

Δ = 25 - 4 \cdot 6

Δ = 25 - 24

Δ = 1

Δ > 0

, the equation has two solutions:

For the first solution, we obtain:

\frac{- b - \sqrt{Δ}}{2 a}

x1 = \frac{- 5 - 1}{2 \cdot (-1)}

ℹ

- 5 - 1

-6

‖

2 \cdot (-1)

-2

x1 = \frac{-6}{-2}

x1 = \frac{6}{2}

x1 = 3

The second solution is:

\frac{- b + \sqrt{Δ}}{2 a}

x2 = \frac{- 5 + 1}{2 \cdot (-1)}

ℹ

- 5 + 1

-4

‖

2 \cdot (-1)

-2

x2 = \frac{-4}{-2}

x2 = \frac{4}{2}

x2 = 2

Solution obtained:

x = 2

Solution found:

x = 3

▶Solution:

x = {2, 3}