Hola

Si los resultados son 1;4

la ecuación es

(x - 1) (x - 4) = 0

x^2 - x - 4 x + 4 = 0

x^2 - 5 x + 4 = 0

Si multiplicamos por 6, nos queda

6 x^2 - 30 x + 24 = 0

6x² - 5x + 6 = 36

6x² - 5x - 30 = 0

6.[x² - (5/6).x - 5] = 0

x² - (5/6).x - 5 = 0

x² - (5/6).x + (5/12)² - (5/12)² - 5 = 0

x² - (5/6).x + (5/12)² - (25/144) - (720/144) = 0

x² - (5/6).x + (5/12)² - (745/144) = 0

x² - (5/6).x + (5/12)² = 745/144

[x - (5/12)]² = [± (√745)/12]²

x - (5/12) = ± (√745)/12

x = (5/12) ± [(√745)/12]

x = (5 ± √745)/12

First case: x = (5 + √745)/12

Second case: x = (5 - √745)/12

6x² + 5x + 6 = 36

6x² + 5x - 30 = 0

6.[x² + (5/6).x - 5] = 0

x² + (5/6).x - 5 = 0

x² + (5/6).x + (5/12)² - (5/12)² - 5 = 0

x² + (5/6).x + (5/12)² - (25/144) - (720/144) = 0

x² + (5/6).x + (5/12)² - (745/144) = 0

x² + (5/6).x + (5/12)² = 745/144

[x + (5/12)]² = [± (√745)/12]²

x + (5/12) = ± (√745)/12

x = - (5/12) ± [(√745)/12]

x = (- 5 ± √745)/12

First case: x = (- 5 + √745)/12

Second case: x = (- 5 - √745)/12

SOLUCIÓN: