Write a quadratic equation in standard form that has two solutions, 5 and 7

If x₁ and x₂ are solutions of the quadratic equation, then we can write it in quadratic factorization:

a (x - x₁) (x - x₂)

We have x₁ = 5 and x₂ = 7

(x - 5) (x - 7) = (x) (x) + (x) (-7) + (-5) (x) + (-5) (-7) = x² - 7x - 5x + 35 = x² - 12x + 35

Answer: x² - 12x + 35 = 0