(x-9)(x)=322

Solution for (x-9)(x)=322 equation:

(x-9)(x)=322

We move all terms to the left:

(x-9)(x)-(322)=0

We multiply parentheses

x^2-9x-322=0

a = 1; b = -9; c = -322;
Δ = b2-4ac
Δ = -92-4·1·(-322)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-37}{2*1}=\frac{-28}{2}
=-14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+37}{2*1}=\frac{46}{2}
=23
$