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