0=144x^2-25x+1

Solution for 0=144x^2-25x+1 equation:

0=144x^2-25x+1

We move all terms to the left:

0-(144x^2-25x+1)=0

We add all the numbers together, and all the variables

-(144x^2-25x+1)=0

We get rid of parentheses

-144x^2+25x-1=0

a = -144; b = 25; c = -1;
Δ = b2-4ac
Δ = 252-4·(-144)·(-1)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-7}{2*-144}=\frac{-32}{-288}
=1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+7}{2*-144}=\frac{-18}{-288}
=1/16
$