How do you solve #\frac { 1} { 4} x ^ { 2} = 3x - \frac { 25} { 2}#?

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Answer 1 · 2018-06-11T15:15:43

no solutions #phi#

#\frac { 1} { 4} x ^ { 2} = 3x - \frac { 25} { 2}#

multiply both sides by 4 to remove the fractions:

#4[\frac { 1} { 4} x ^ { 2} = 3x - \frac { 25} { 2}]#

#x^2=12x-50#

#x^2-12x+50=0#

If we check the discriminant of the form #ax^2+bx+c#:

#b^2-4ac#

#(-12)^2-4*1*50=-56#

Since the discriminant is negative there are no real solutions to this polynomial as can be seen from its graph:

graph{x^2-12x+50 [-35.17, 44.83, -3.52, 36.48]}