x2-2x=146

Solution for x2-2x=146 equation:

x2-2x=146

We move all terms to the left:

x2-2x-(146)=0

We add all the numbers together, and all the variables

x^2-2x-146=0

a = 1; b = -2; c = -146;
Δ = b2-4ac
Δ = -22-4·1·(-146)
Δ = 588
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:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-14\sqrt{3}}{2*1}=\frac{2-14\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14\sqrt{3}}{2*1}=\frac{2+14\sqrt{3}}{2}
$