Find the positive difference between the solutions to the equation 6t^2 + 30 = 41t + 7t - 2t^2.
+23252 6t2 + 30 = 41t + 7t - 2t2
1) Simplify the right side: 6t2 + 30 = 48t - 2t2
2) Get all the terms to the left side: 6t2 + 30 - 48t + 2t2 = 0
3) Simplify the left side: 8t2 - 48t + 30 = 0 ---> 4t2 - 24t + 15 = 0
4) Use the quadratic formula to get the two solutions:
x = [ 24 + sqrt( (-24)2 - 4(4)(15) ) ] / (2·4) = [ 24 + sqrt(336) ] / 8
= [ 24 + 4sqrt(21) ] / 8 = [ 6 + sqrt(21) ] / 2
and x = [ 6 - sqrt(21) ] / 2
7) Finish by subtracting the smaller solution from the larger solution.
