x(x-2)=670

Solution for x(x-2)=670 equation:

x(x-2)=670

We move all terms to the left:

x(x-2)-(670)=0

We multiply parentheses

x^2-2x-670=0

a = 1; b = -2; c = -670;
Δ = b2-4ac
Δ = -22-4·1·(-670)
Δ = 2684
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:

$\sqrt{\Delta}=\sqrt{2684}=\sqrt{4*671}=\sqrt{4}*\sqrt{671}=2\sqrt{671}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{671}}{2*1}=\frac{2-2\sqrt{671}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{671}}{2*1}=\frac{2+2\sqrt{671}}{2}
$