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.