(x-3)(x+5)=320

Solution for (x-3)(x+5)=320 equation:

(x-3)(x+5)=320

We move all terms to the left:

(x-3)(x+5)-(320)=0

We multiply parentheses ..

(+x^2+5x-3x-15)-320=0

We get rid of parentheses

x^2+5x-3x-15-320=0

We add all the numbers together, and all the variables

x^2+2x-335=0

a = 1; b = 2; c = -335;
Δ = b2-4ac
Δ = 22-4·1·(-335)
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-8\sqrt{21}}{2*1}=\frac{-2-8\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8\sqrt{21}}{2*1}=\frac{-2+8\sqrt{21}}{2}
$