What is the answer to |x-8|=|3x^2-5|-|2x+3| ?

The answer to |x-8|=|3x^2-5|-|2x+3| is x=(-3-sqrt(129))/6 \lor x=(1+sqrt(193))/6

Solve for x: |x-8|=|3x^2-5|-|2x+3|

The solution is x=(-3-sqrt(129))/6 \lor x=(1+sqrt(193))/6

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∣ x - 8 ∣ = 3 x^{2} - 5 - ∣ 2 x + 3 ∣

x = \frac{- 3 - 129}{6} or x = \frac{1 + 193}{6}

Decimal Notation

x = - 2.39296 \dots, x = 2.48207 \dots

Solution steps

∣ x - 8 ∣ = 3 x^{2} - 5 - ∣ 2 x + 3 ∣

Find positive and negative intervals

x < - \frac{3}{2}, - \frac{3}{2} \leq x \leq - \frac{5}{3}, - \frac{5}{3} < x < \frac{5}{3}, \frac{5}{3} \leq x < 8, x \geq 8

Solve the inequality for each interval

x = \frac{- 3 - 129}{6} or No Solution or x = \frac{1 + 193}{6}

x = \frac{- 3 - 129}{6} or x = \frac{1 + 193}{6}

3 ∣ x + 2 ∣ - x = 3

∣ x - 5 ∣^{2} + ∣ x - 5 ∣ - 24 = 0

1 x^{2} - x + ∣ x + 1 ∣ = 5

∣ 3 x + 2 ∣ = x + 1, ∣ 2 x - 3 ∣ = x - 5, ∣ 3 x - 2 ∣ = 2 x + 3

y, 17 x^{2} - 16 ∣ x ∣ y + 17 y^{2} = 225

What is the answer to |x-8|=|3x^2-5|-|2x+3| ?
The answer to |x-8|=|3x^2-5|-|2x+3| is x=(-3-sqrt(129))/6 \lor x=(1+sqrt(193))/6
Solve for x: |x-8|=|3x^2-5|-|2x+3|
The solution is x=(-3-sqrt(129))/6 \lor x=(1+sqrt(193))/6