Write the equation that shows the quadratic formula is used correctly to solve 5x² + 3x - 4 = 0 for x.

Solution:

Quadratic equations are second-degree algebraic expressions and are of the form ax² + bx + c = 0.

Given: A quadratic equation, 5x² + 3x - 4 = 0

According to the given equation 5x² + 3x - 4 = 0,

a = 5, b = 3, c = -4

We will be using the quadratic formula to calculate the value of x.

x = [−b ± √(b² - 4ac)] / 2a

Substituting the values of a, b and c we get,

x = [-3 ± √{3² - 4 × 5 × (-4)}] / (2 × 5)

x = (-3 ± √89) / 10

Thus, the two values of x are:

x = (-3 + √89) / 10 and x = (-3 - √89) / 10

We can also use Cuemath's Online Quadratic equation calculator to find the roots of an equation.

Thus, the equation that shows the quadratic formula is used correctly to solve 5x² + 3x - 4 = 0 for x is x = [-3 ± √{3² - 4 × 5 × (-4)}] / (2 × 5).