(x)(x-6)=80^2

Solution for (x)(x-6)=80^2 equation:

(x)(x-6)=80^2

We move all terms to the left:

(x)(x-6)-(80^2)=0

We add all the numbers together, and all the variables

x(x-6)-6400=0

We multiply parentheses

x^2-6x-6400=0

a = 1; b = -6; c = -6400;
Δ = b2-4ac
Δ = -62-4·1·(-6400)
Δ = 25636
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:

$\sqrt{\Delta}=\sqrt{25636}=\sqrt{4*6409}=\sqrt{4}*\sqrt{6409}=2\sqrt{6409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{6409}}{2*1}=\frac{6-2\sqrt{6409}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{6409}}{2*1}=\frac{6+2\sqrt{6409}}{2}
$