X^2-60x+900=x

Solution for X^2-60x+900=x equation:

X^2-60X+900=X

We move all terms to the left:

X^2-60X+900-(X)=0

We add all the numbers together, and all the variables

X^2-61X+900=0

a = 1; b = -61; c = +900;
Δ = b2-4ac
Δ = -612-4·1·900
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-61)-11}{2*1}=\frac{50}{2}
=25
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-61)+11}{2*1}=\frac{72}{2}
=36
$