Sure, let's find the solutions to the equation 4x² - 24x + 20 = 0.
We know that the standard form of the quadratic equation is ax² + bx + c = 0. We can apply the quadratic formula to solve for x, which is x = [-b ± sqrt(b² - 4ac)] / (2a).
In the given equation:
- a is 4,
- b is -24,
- c is 20.
Now, let's calculate the discriminant first. The discriminant (D) of a quadratic equation is found using the formula D = b² - 4ac.
So, D = (-24)² - 4*4*20 = 576 - 320 = 256.
The discriminant is positive, so we have two distinct real roots.
Now we will use the quadratic formula to solve for x.
We have two possible solutions for x, given as:
x₁ = [-(-24) + √256] / 2*4 = (24 + 16) / 8 = 40 / 8 = 5,
x₂ = [-(-24) - √256] / 2*4 = (24 - 16) / 8 = 8 / 8 = 1.
So, the solutions to the quadratic equation 4x² - 24x + 20 = 0 are x₁ = 5 and x₂ = 1.