2x-1=x^2-16x+64

Solution for 2x-1=x^2-16x+64 equation:

2x-1=x^2-16x+64

We move all terms to the left:

2x-1-(x^2-16x+64)=0

We get rid of parentheses

-x^2+2x+16x-64-1=0

We add all the numbers together, and all the variables

-1x^2+18x-65=0

a = -1; b = 18; c = -65;
Δ = b2-4ac
Δ = 182-4·(-1)·(-65)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-8}{2*-1}=\frac{-26}{-2}
=+13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+8}{2*-1}=\frac{-10}{-2}
=+5
$