x(x-280)=450

Solution for x(x-280)=450 equation:

x(x-280)=450

We move all terms to the left:

x(x-280)-(450)=0

We multiply parentheses

x^2-280x-450=0

a = 1; b = -280; c = -450;
Δ = b2-4ac
Δ = -2802-4·1·(-450)
Δ = 80200
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:

$\sqrt{\Delta}=\sqrt{80200}=\sqrt{100*802}=\sqrt{100}*\sqrt{802}=10\sqrt{802}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-280)-10\sqrt{802}}{2*1}=\frac{280-10\sqrt{802}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-280)+10\sqrt{802}}{2*1}=\frac{280+10\sqrt{802}}{2}
$