How do you solve 6tanx2-17tanx plus 7 equals 0?

Answer 1

Assuming your equation is: 6(tanx)2-17tanx + 7 = 0

The easiest way to do it is use a substitution. Let s=tanx, then substitute s for tanx in the original equation to get the following:

6s2-17s+7=0

Using the quadratic equation solve for s:

s = {-(-17) +- SQRT [(-17)2 - 4*(6)*7)]}/(2*6)

s = [17 + SQRT (121)]/12 & s= [17 - SQRT(121)]/12

s = 28/12 or 7/3 & s = 6/12 or 1/2

Now substitute tanx back for s to get

tan x = 7/3 & tan x = 1/2

x = tan-1(7/3) or approx. 66.8o & x= tan-1(1/2) or approx. 26.6o

In radians it would be 1.166 & 0.4636