Solve 6x2 = 12x - 20.

If you are using the first X as a multiplication sign and the second as a variable the answer is 8/3 but if both are meant to be variables and the 2 is an exponent the answer is No real solutions

6x^2=12x-20 subtract 12x from both sides

6x^2-12x=-20 divide both sides by 6

x^2-2x=-10/3 halve the linear coefficient, square it, and add it to both sides, in this case 1

x^2-2x+1=3/3-10/3 now the left sides is a perfect square

(x-1) ^2=-7/3 take the square root of both sides

x-1=±i√ (7/3) add 1 to both sides

x=1±i√ (7/3)

*note that these are imaginary solutions, as the original equation is never true, or if you prefer, 6x^2-12x+20 is never equal to zero.