42x^2-69x+20=7x^2-8
35x^2 - 69x + 28 = 0
(5x-7)(7x - 4) = 0
x = 7/5 or x = 4/7
To solve the given quadratic equation: 42x^2 - 69x + 20 = 7x^2 - 8, we need to bring all the terms to one side of the equation and set it equal to zero.
Rearranging the equation:
42x^2 - 69x + 20 - 7x^2 + 8 = 0
Combining like terms:
35x^2 - 69x + 28 = 0
Now, we have a quadratic equation in the standard form: ax^2 + bx + c = 0. Comparing the coefficients, we have:
a = 35, b = -69, c = 28
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values:
x = (-(-69) ± √((-69)^2 - 4 * 35 * 28)) / (2 * 35)
Simplifying further:
x = (69 ± √(4761 - 3920)) / 70
x = (69 ± √840) / 70
Now, we need to find the square root of 840. Using a calculator, we find:
√840 ≈ ±28.98
Therefore, we have two potential solutions:
x1 = (69 + 28.98) / 70 ≈ 1.28
x2 = (69 - 28.98) / 70 ≈ 0.57
So, the solutions to the given quadratic equation are approximately x = 1.28 and x = 0.57.