x^2-6x+9=10000

Solution for x^2-6x+9=10000 equation:

x^2-6x+9=10000

We move all terms to the left:

x^2-6x+9-(10000)=0

We add all the numbers together, and all the variables

x^2-6x-9991=0

a = 1; b = -6; c = -9991;
Δ = b2-4ac
Δ = -62-4·1·(-9991)
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-200}{2*1}=\frac{-194}{2}
=-97
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+200}{2*1}=\frac{206}{2}
=103
$