Solve for x cube root of 5x^2+7x-4- cube root of 8x=0

$\sqrt[3]{5 x^{2} + 7 x - 4} - \sqrt[3]{8 x} = 0$

Simplify each term.

Rewrite $8$ as $2^{3}$ .

$\sqrt[3]{5 x^{2} + 7 x - 4} - \sqrt[3]{2^{3} x} = 0$

Pull terms out from under the radical.

$\sqrt[3]{5 x^{2} + 7 x - 4} - (2 \sqrt[3]{x}) = 0$

Multiply $2$ by $- 1$ .

$\sqrt[3]{5 x^{2} + 7 x - 4} - 2 \sqrt[3]{x} = 0$

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = - \frac{4}{5}, 1$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{4}{5}, 1$

Decimal Form:

$x = - 0.8, 1$