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It is very simple..

a + b = 25

a = 25 - b ---- equation 1

now a b = 6 substitute the value of a from equation 1 in this equation

(25 - b) b = 6

25 b - b² = 6 take all the terms to RHS

b² -25 b + 6 = 0

this is solved using standard quadratic equation rules.

Δ = 25² - 6*4 = 625 - 24 = 601

b = (25 +- 24.51 ) / 2 = 0.49/2 or 49.51/2

b = 0.245 or 24.755 pair a,b is = 0.245 & 24.755 OR 24.755 & 0.245

a = 24.755 or 0.245

a + b = 25

a = 25 - b ---- equation 1

now a b = 6 substitute the value of a from equation 1 in this equation

(25 - b) b = 6

25 b - b² = 6 take all the terms to RHS

b² -25 b + 6 = 0

this is solved using standard quadratic equation rules.

Δ = 25² - 6*4 = 625 - 24 = 601

b = (25 +- 24.51 ) / 2 = 0.49/2 or 49.51/2

b = 0.245 or 24.755 pair a,b is = 0.245 & 24.755 OR 24.755 & 0.245

a = 24.755 or 0.245