5x^2+x+4=0 — step-by-step solution

Let's solve in

ℝ

5 x^{2} + x + 4 = 0

Given the quadratic form

a x^{2} + b x + c

, let's compute the discriminant:

Δ = b^{2} - 4 a c

. Here

a = 5

b = 1

and

c = 4

Δ = 1 - 4 \cdot 5 \cdot 4

ⓘ Multiplications are done before additions and subtractions:

5 \cdot 4

20

Δ = 1 - 20 \cdot 4

ⓘ Multiplications are done before additions and subtractions:

20 \cdot 4

80

Δ = 1 - 80

ⓘ Start from

1

and move back

80

on the number line, going below zero:

1 - 80

-79

Δ = -79

Δ < 0

, the equation has no real root.

▶Solution:

x \in \emptyset