x^2+3x+7=(x+3/2)^2+(7-9/4)>0 Vx
4x^2-x(2a-9)+30>0
D<0
(2a-9)^2-16*30
4a^2+81-36a-30*16<0
4a^2-36a-399<0
a=(18+-√(324+1596))/4
a=(18+-√1920)/4=(9+-4√30)/2
a ((9-4√30)/2;(9+4√30)/2)
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Answers & Comments
x^2+3x+7=(x+3/2)^2+(7-9/4)>0 Vx
4x^2-x(2a-9)+30>0
D<0
(2a-9)^2-16*30
4a^2+81-36a-30*16<0
4a^2-36a-399<0
a=(18+-√(324+1596))/4
a=(18+-√1920)/4=(9+-4√30)/2
a ((9-4√30)/2;(9+4√30)/2)