(x-9)(2x)=442

Solution for (x-9)(2x)=442 equation:

(x-9)(2x)=442

We move all terms to the left:

(x-9)(2x)-(442)=0

We multiply parentheses

2x^2-18x-442=0

a = 2; b = -18; c = -442;
Δ = b2-4ac
Δ = -182-4·2·(-442)
Δ = 3860
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:

$\sqrt{\Delta}=\sqrt{3860}=\sqrt{4*965}=\sqrt{4}*\sqrt{965}=2\sqrt{965}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{965}}{2*2}=\frac{18-2\sqrt{965}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{965}}{2*2}=\frac{18+2\sqrt{965}}{4}
$