37.5=30*a+(4-a)/4*30*a

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Solution for 37.5=30*a+(4-a)/4*30*a equation:


a in (-oo:+oo)

37.5 = 30*a*((4-a)/4)+30*a // - 30*a*((4-a)/4)+30*a

37.5-(30*a*((4-a)/4))-(30*a) = 0

(-15/2)*a*(4-a)-30*a+37.5 = 0

37.5-15/2*a*(4-a)-30*a = 0

37.5-15/2*a*(4-a)-30*a = 0

15/2*a^2-60*a+37.5 = 0

15/2*a^2-60*a+37.5 = 0

15/2*a^2-60*a+37.5 = 0

DELTA = (-60)^2-(4*15/2*37.5)

DELTA = 2475

DELTA > 0

a = (2475^(1/2)+60)/(2*15/2) or a = (60-2475^(1/2))/(2*15/2)

a = (15*11^(1/2)+60)/15 or a = (60-15*11^(1/2))/15

(a-((60-15*11^(1/2))/15))*(a-((15*11^(1/2)+60)/15)) = 0

(a-((60-15*11^(1/2))/15))*(a-((15*11^(1/2)+60)/15)) = 0

( a-((15*11^(1/2)+60)/15) )

a-((15*11^(1/2)+60)/15) = 0 // + (15*11^(1/2)+60)/15

a = (15*11^(1/2)+60)/15

( a-((60-15*11^(1/2))/15) )

a-((60-15*11^(1/2))/15) = 0 // + (60-15*11^(1/2))/15

a = (60-15*11^(1/2))/15

a in { (15*11^(1/2)+60)/15, (60-15*11^(1/2))/15 }

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