Solve the equation and verify your answer: `(7x-2)/(5x-1)=(3x-4)/(x+6)`

Explanation

`(7x-2)/(5x-1)=(3x-4)/(x+6)`
`(7x-2)(x+6)=(3x-4)(5x-1)`
`x(7x-2)+6(7x-2)=5x(3x-4)-1(3x-4)`
`7x^2-2x+42x-12=15x^2-20x-3x+4`
`7x^2-15x^2+40x-12= -23x+4`
`-8x^2+63x-16=0`
`8x^2-63x+16=0`
Using
`x=-b pm sqrt (b^2-4ac)/(2a)`
`x=(-(-63)pm sqrt {(-63)^2-4xx8xx6)}/(2xx8)`
`x=63 pm sqrt (3969-512)/(16)`
`x=(63 pm sqrt 3457)/(16)`.