2x^2=-6+8x — step-by-step solution

⚠Ⓘ 2x is read as the product 2*x: for a power, write 2^x‖8x is read as the product 8*x: for a power, write 8^x

1) Let's solve in

ℝ

2 x^{2} = - 6 + 8 x

You can factorize this expression into:

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

2) Let's solve:

x^{2} + 3 - 4 x = 0

Given the quadratic form

a x^{2} + b x + c

, let's compute the discriminant:

Δ = b^{2} - 4 a c

Δ = {(-4)}^{2} - 4 \cdot 1 \cdot 3

Δ = 16 - 4 \cdot 3

Δ = 16 - 12

Δ = 4

Δ > 0

, the equation has two solutions:

For the first solution, we obtain:

\frac{- b - \sqrt{Δ}}{2 a}

x1 = \frac{4 - \sqrt{4}}{2}

x1 = \frac{4 - 2}{2}

x1 = \frac{2}{2}

x1 = 1

For the second solution, we obtain:

\frac{- b + \sqrt{Δ}}{2 a}

x2 = \frac{4 + \sqrt{4}}{2}

x2 = \frac{4 + 2}{2}

x2 = \frac{6}{2}

x2 = 3

Solution obtained:

x = 1

Solution found:

x = 3

▶Solution:

x = {1, 3}