x2-144=x

Solution for x2-144=x equation:

x2-144=x

We move all terms to the left:

x2-144-(x)=0

We add all the numbers together, and all the variables

x^2-1x-144=0

a = 1; b = -1; c = -144;
Δ = b2-4ac
Δ = -12-4·1·(-144)
Δ = 577
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{-(-1)-\sqrt{577}}{2*1}=\frac{1-\sqrt{577}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{577}}{2*1}=\frac{1+\sqrt{577}}{2}
$