Solve the equation simplify all irrational solutions 5x^2+14x=x+6
A X={-3,2/5}
B x={3,5}
C x={15,5}
D x={2/3,3}
To solve the equation 5x^2 + 14x = x + 6, we need to set it equal to zero first by subtracting x and 6 on both sides.
5x^2 + 13x - 6 = 0
Now, we need to factorize the quadratic equation:
(5x - 2)(x + 3) = 0
Setting each factor equal to zero gives:
5x - 2 = 0 -> 5x = 2 -> x = 2/5
x + 3 = 0 -> x = -3
Therefore, the solutions to the equation are x = -3 and x = 2/5 which matches option A: x={-3,2/5}.