x(x-3)=418

Solution for x(x-3)=418 equation:

x(x-3)=418

We move all terms to the left:

x(x-3)-(418)=0

We multiply parentheses

x^2-3x-418=0

a = 1; b = -3; c = -418;
Δ = b2-4ac
Δ = -32-4·1·(-418)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-41}{2*1}=\frac{-38}{2}
=-19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+41}{2*1}=\frac{44}{2}
=22
$