(2x-8)(x+3)=322

Solution for (2x-8)(x+3)=322 equation:

(2x-8)(x+3)=322

We move all terms to the left:

(2x-8)(x+3)-(322)=0

We multiply parentheses ..

(+2x^2+6x-8x-24)-322=0

We get rid of parentheses

2x^2+6x-8x-24-322=0

We add all the numbers together, and all the variables

2x^2-2x-346=0

a = 2; b = -2; c = -346;
Δ = b2-4ac
Δ = -22-4·2·(-346)
Δ = 2772
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:

$\sqrt{\Delta}=\sqrt{2772}=\sqrt{36*77}=\sqrt{36}*\sqrt{77}=6\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{77}}{2*2}=\frac{2-6\sqrt{77}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{77}}{2*2}=\frac{2+6\sqrt{77}}{4}
$