Solve: `6x^(2)+40=31x.`

Explanation

The given equation may be written as `6x^(2)-31x+40=0.`
We write,
`-31x=-16x-15x" as "6x^(2)xx40=240x^(2)=(-16x)xx(-15x).`
`:." "6x^(2)-31x+40=0`
`implies" "6x^(2)-16x-15x+40=0implies2x(3x-8)-5(3x-8)=0`
`implies" "(3x-8)(2x-5)=0implies3x-8=0" or "2x-5=0`
`implies" "x=(8)/(3)" or "x=(5)/(2).`
Hence, `(8)/(3)" and "(5)/(2)` are the roots of the given equation.