What is x in this equation equal

Question

solve and check  6x^2+1=5x

thanks.

Answer 1

6x^2 + 1 = 5x

Subtract 5x  from each side.

6x^2 + 1 - 5x  = 0

6x^2 - 5x + 1 = 0

6x^2 - 2x - 3x + 1 = 0

2x(3x - 1) - 1(3x - 1) = 0

Take common out (3x - 1) from above equation.

(3x - 1)(2x - 1) = 0

3x - 1 = 0

Add 1 to each side.

3x = 1

Divide each side by 3.

x = 1/3

And 2x - 1 = 0

Add 1 to each side.

2x  = 1

Divide each side by 2.

x = 1/2

Solution x = 1/2 and 1/3.

Check :

Equation 6x^2 + 1 = 5x

If x = 1/2

6(1/4) +1 = 5/2

3/2 + 1 = 5/2

5/2 = 5/2

If x  = 1/3

6(1/9) + 1 = 5/3

2/3 + 1 = 5/3

5/3 = 5/3.