What is the answer to |3x-4|=x^2 ?

The answer to |3x-4|=x^2 is x=-4\lor x=1

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|3x-4|=x^2

∣ 3 x - 4 ∣ = x^{2}

x = - 4 or x = 1

Solution steps

∣ 3 x - 4 ∣ = x^{2}

Find positive and negative intervals

x < \frac{4}{3}, x \geq \frac{4}{3}

Solve the inequality for each interval

(x = - 4 or x = 1) or No Solution

x = - 4 or x = 1

0 = ∣ x - 1 ∣ - 2

\frac{x}{3} + 4 = 5

∣ v ∣ = 2

x, ∣ x - y ∣ = 1

∣ 2 x + 2 ∣ + 1 = 3