12-4x+24x^2=0 — step-by-step solution

⚠ 4x is read as the product 4*x: for a power, write 4^x

⚠ 24x is read as the product 24*x: for a power, write 24^x

Let's solve in

ℝ

12 - 4 x + 24 x^{2} = 0

You can write the expression in factored form:

4 \cdot (3 - x + 6 x^{2}) = 0

Let's solve:

3 - 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 = {(-1)}^{2} - 4 \cdot 6 \cdot 3

ℹ

{(-1)}^{2}

1

‖

4 \cdot 6

24

Δ = 1 - 24 \cdot 3

Δ = 1 - 72

Δ = -71

Since

Δ < 0

, the equation has no solution.

No solution in

ℝ

for:

x

▶Solution:

x \in \emptyset