# Solve the following algebraic equation: |2x^2-x|=2x^2-x+8?

Jun 20, 2016

$x = \frac{1}{4} \left(1 \pm i \sqrt{31}\right)$

#### Explanation:

Making $y = 2 {x}^{2} - x$ we have

$\left\mid y \right\mid - y = 8$

with solution $y = - 4$

Now following with

$y = 2 {x}^{2} - x = - 4$

we have the solutions

$x = \frac{1}{4} \left(1 \pm i \sqrt{31}\right)$