Solve $2x^2-5x+2=$ $\frac{5-\sqrt{9+8x}}{4}$ Solve $2x^2-5x+2$= $\frac{5-\sqrt{9+8x}}{4}$
I simply do square both sides solve it and I get two value of x one is 2 and other is $\frac{3-√5}{2}$ but this approach it take more time so is there any approach for solving this equation.

Taking Jerry Chang's observation (which amounts to the fact that the expression on the right-hand side is what you get when you plug the coefficients of the quadratic into the quadratic formula, just choosing the minus sign for the square root) and setting $y=2x^2-5x+2$ so that $x=2y^2-5y+2$ we can subtract one of these from the other to obtain:
$$y-x=2(x^2-y^2)-5(x-y)$$
Which yields $y=x$ ; or
$1=5-2(x+y)$ ie $x+y=2$
Then the problem splits as $2x^2-5x+2=x$ or $2x^2-5x+2=2-x$
The solutions of these equations have to be plugged back into the original for checking to see which belongs to which choice of sign of the square root.
