Answer:
3x^2 - 20x = 7 are x = 7 and x = -1/3.
Step-by-step explanation:
To solve the quadratic equation 3x^2 - 20x = 7 using the quadratic formula, we need to first rewrite the equation in the standard form ax^2 + bx + c = 0.
Given equation: 3x^2 - 20x = 7
Subtracting 7 from both sides to set the equation equal to zero:
3x^2 - 20x - 7 = 0
Now, we can identify a = 3, b = -20, and c = -7 in the quadratic formula:
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a
Substitute the values of a, b, and c into the formula:
x = (20 ± √((-20)^2 - 4*3*(-7))) / (2*3)
x = (20 ± √(400 + 84)) / 6
x = (20 ± √484) / 6
x = (20 ± 22) / 6
Now, we have two possible solutions:
1. x = (20 + 22) / 6 = 42 / 6 = 7
2. x = (20 - 22) / 6 = -2 / 6 = -1/3
Therefore, the solutions to the equation 3x^2 - 20x = 7 are x = 7 and x = -1/3.
