2x^2-24x+80=0 — step-by-step solution

Let's solve in

ℝ

2 x^{2} - 24 x + 80 = 0

Since

2 \neq 0

, divide both sides by

2

x^{2} - 12 x + 40 = 0

Given the quadratic form

a x^{2} + b x + c

, let's compute the discriminant:

Δ = b^{2} - 4 a c

. Here

a = 1

b = -12

and

c = 40

Δ = {(-12)}^{2} - 4 \cdot 1 \cdot 40

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

{(-12)}^{2}

(-12) \cdot (-12)

144

Δ = 144 - 4 \cdot 40

ⓘ Multiplications are done before additions and subtractions:

4 \cdot 40

160

Δ = 144 - 160

ⓘ Start from

144

and move back

160

on the number line, going below zero:

144 - 160

-16

Δ = -16

Δ < 0

, the equation has no real root.

▶Solution:

x \in \emptyset