((9-4k^2)+(1+16k^2))^1/2=50

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Solution for ((9-4k^2)+(1+16k^2))^1/2=50 equation: 


k in (-oo:+oo)

((16*k^2-(4*k^2)+1+9)^1)/2 = 50 // - 50

((16*k^2-(4*k^2)+1+9)^1)/2-50 = 0

(16*k^2-4*k^2+1+9)/2-50 = 0

(12*k^2+10)/2-50 = 0

(12*k^2+10)/2+(-50*2)/2 = 0

12*k^2-50*2+10 = 0

12*k^2-90 = 0

(12*k^2-90)/2 = 0

(12*k^2-90)/2 = 0 // * 2

12*k^2-90 = 0

12*k^2 = 90 // : 12

k^2 = 15/2

k^2 = 15/2 // ^ 1/2

abs(k) = (15/2)^(1/2)

k = (15/2)^(1/2) or k = -(15/2)^(1/2)

k in { (15/2)^(1/2), -(15/2)^(1/2) }

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