5x^2=x-2 — step-by-step solution

Let's solve in

ℝ

5 x^{2} = x - 2

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

Given the quadratic form

a x^{2} + b x + c

, you can calculate the discriminant:

Δ = b^{2} - 4 a c

. Here

a = 5

b = -1

and

c = 2

Δ = {(-1)}^{2} - 4 \cdot 5 \cdot 2

ⓘ Powers are computed before multiplications, additions and subtractions. An integer power is a repeated product:

{(-1)}^{2}

(-1) \cdot (-1)

1

■Multiplications are done before additions and subtractions:

4 \cdot 5

20

Δ = 1 - 20 \cdot 2

ⓘ Multiplications are done before additions and subtractions:

20 \cdot 2

40

Δ = 1 - 40

ⓘ Start from

1

and move back

40

on the number line, going below zero:

1 - 40

-39

Δ = -39

Δ < 0

, the equation has no real root.

▶Solution:

x \in \emptyset