0=2x^2-53.73x+64

Solution for 0=2x^2-53.73x+64 equation:

0=2x^2-53.73x+64

We move all terms to the left:

0-(2x^2-53.73x+64)=0

We add all the numbers together, and all the variables

-(2x^2-53.73x+64)=0

We get rid of parentheses

-2x^2+53.73x-64=0

a = -2; b = 53.73; c = -64;
Δ = b2-4ac
Δ = 53.732-4·(-2)·(-64)
Δ = 2374.9129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53.73)-\sqrt{2374.9129}}{2*-2}=\frac{-53.73-\sqrt{2374.9129}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53.73)+\sqrt{2374.9129}}{2*-2}=\frac{-53.73+\sqrt{2374.9129}}{-4}
$