x^2-2x+15=195

Solution for x^2-2x+15=195 equation:

x^2-2x+15=195

We move all terms to the left:

x^2-2x+15-(195)=0

We add all the numbers together, and all the variables

x^2-2x-180=0

a = 1; b = -2; c = -180;
Δ = b2-4ac
Δ = -22-4·1·(-180)
Δ = 724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{181}}{2*1}=\frac{2-2\sqrt{181}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{181}}{2*1}=\frac{2+2\sqrt{181}}{2}
$