x(x-2)=675

Solution for x(x-2)=675 equation:

x(x-2)=675

We move all terms to the left:

x(x-2)-(675)=0

We multiply parentheses

x^2-2x-675=0

a = 1; b = -2; c = -675;
Δ = b2-4ac
Δ = -22-4·1·(-675)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-52}{2*1}=\frac{-50}{2}
=-25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+52}{2*1}=\frac{54}{2}
=27
$