I need help writing an equation like this.

Question

The height of a rectangular box is 6ft. The length is 2ft longer that thrice the width x. The volume is 510ft^3

Answer 1

Width w = x

Length L = 3x+2

Volume V = L*w*h = 6*x*(3x+2) = 510

x(3x+2) = 510/6 = 170/2 = 85

3x^2 + 2x - 85 = 0

( 3x + 17 )( x - 5 ) = 0

3x+17=0 results in negative measures

x-5 = 0 --> x = 5 is the width

length = 3(5)+2 = 15+2 = 17

6*5*17 = 30*17 = 510