Solve `sqrt(3x^2-7x-30)+sqrt(2x^2-7x-5)=x+5.`

Answer

`x = 6, - 5//2`

Explanation

`sqrt(3x^(2) - 7x - 30) + sqrt(2x^(2) - 7x - 5) = x + 5`
or `sqrt(3x^(2) - 7x - 30) =(x+5)- sqrt(2x^(2) - 7x - 5) = `
or On squaring, we get
`3x^(2) - 7x - 30 =x^(2) + 10x + 25 - 2(x+5) xxsqrt(2x^(2) - 7x - 5)+ 2x^(2) - 7x - 5`
or `10x + 50 = 2(x + 5) sqrt(2x^(2) - 7x - 5)`
`rArr x = - 5 or sqrt(2x^(2) - 7x - 5) = 5`
`rArr x = - 5 or 2x^(2) - 7x - 30 = 0`
`rArr x = - 5 or x = 6 or x = - 5//2`
But `x = - 5` does not satisfy the original equation.