5x^2+x+1=0 — step-by-step solution

Let's solve in

ℝ

5 x^{2} + x + 1 = 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 = 1

Δ = 1 - 4 \cdot 5 \cdot 1

Δ = 1 - 4 \cdot 5

ⓘ Multiplications are done before additions and subtractions:

4 \cdot 5

20

Δ = 1 - 20

ⓘ Start from

1

and move back

20

on the number line, going below zero:

1 - 20

-19

Δ = -19

Δ < 0

, the equation has no real root.

▶Solution:

x \in \emptyset